It is currently 21 Oct 2017, 05:55

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the lowest positive integer that is divisible by

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129095 [0], given: 12194

What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 11 Sep 2012, 04:43
Expert's post
23
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

69% (00:44) correct 31% (00:53) wrong based on 1461 sessions

HideShow timer Statistics

What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?

(A) 420
(B) 840
(C) 1,260
(D) 2,520
(E) 5,040

Practice Questions
Question: 40
Page: 157
Difficulty: 600
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129095 [0], given: 12194

Expert Post
4 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129095 [4], given: 12194

Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 11 Sep 2012, 04:43
4
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
SOLUTION

What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?

(A) 420
(B) 840
(C) 1,260
(D) 2,520
(E) 5,040

The integer should be divisible by: 2, 3, 4(=2^2), 5, 6(=2*3), and 7. The least common multiple of these integers is LCM=2^2*3*5*7=420.

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129095 [4], given: 12194

1 KUDOS received
Manager
Manager
avatar
Joined: 12 Mar 2012
Posts: 164

Kudos [?]: 61 [1], given: 4

Location: India
Concentration: Technology, General Management
GMAT Date: 07-23-2012
WE: Programming (Telecommunications)
Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 11 Sep 2012, 09:24
1
This post received
KUDOS
Factors of 420 are: 1, 2, 2, 3, 5, 7

Now 420 should be divided by each of 1, 2, 3, 4, 5, 6, 7

From the factors which we get above by factorization and combining them to make all numbers from 1 to 7,

420 divided by 1
420 divided by 2 (picking up from factors)
420 divided by 3 (picking up from factors)
420 divided by 4 (picking up two 2s and multiplying to make it 4)
420 divided by 5 (picking up from factors)
420 divided by 6 (picking up 2 and 3 from factors and multiplying to make it 6)
420 divided by 7 (picking up from factors)
All leaves remainder as ZERO.

No need to go further. Answer is A.
_________________

FOCUS..this is all I need!

Ku-Do!

Kudos [?]: 61 [1], given: 4

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 06 Aug 2011
Posts: 390

Kudos [?]: 235 [1], given: 82

Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 11 Sep 2012, 10:04
1
This post received
KUDOS
1
This post was
BOOKMARKED
its A..

1*2*3*2*5*7=420...
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

Kudos [?]: 235 [1], given: 82

1 KUDOS received
Intern
Intern
avatar
Status: Life begins at the End of your Comfort Zone
Joined: 31 Jul 2011
Posts: 47

Kudos [?]: 33 [1], given: 4

Location: Tajikistan
Concentration: General Management, Technology
GPA: 3.86
Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 11 Sep 2012, 10:07
1
This post received
KUDOS
Here are the integers from 1 to 7 including: 1, 2, 3, 4, 5, 6, 7
So the lowest positive integer divisible by every single numbers set forth above would have to be divisible by 7,5,4,3 simultaneously or 7*5*4*3=420
please, correct me if I went awry
_________________

God loves the steadfast.

Kudos [?]: 33 [1], given: 4

2 KUDOS received
Senior Manager
Senior Manager
avatar
B
Joined: 24 Aug 2009
Posts: 499

Kudos [?]: 839 [2], given: 276

Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 12 Sep 2012, 12:26
2
This post received
KUDOS
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
(A) 420
(B) 840
(C) 1,260
(D) 2,520
(E) 5,040

The question is basically asking the LCM (smallest multiple) of number from 1 to 7 (both inclusive)

LCM of 1,2,3,4,5,6,7 = 420
Answer A

Hope it helps
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Kudos [?]: 839 [2], given: 276

4 KUDOS received
Current Student
User avatar
Joined: 27 Jun 2012
Posts: 405

Kudos [?]: 932 [4], given: 184

Concentration: Strategy, Finance
Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 13 Jan 2013, 23:43
4
This post received
KUDOS
2
This post was
BOOKMARKED
You need LCM of first 7 numbers, NOT factorial. If a number is divisible by 6 then its also divisible by 2 & 3. You dont have to count 2 & 3 again when you consider factor as 6.

\(1=1^1\)
\(2=2^1\)
\(3=3^1\)
\(4=2^2\)
\(5=5^1\)
\(6=2^1 *3^1\)
\(7=7^1\)

\(LCM =1^1 * 2^2 * 3^1 * 5^1 * 7^1= 420\)

Hence choice(A) is the answer.
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
Reading Comprehension notes: Click here
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here
Looking to finance your tuition: Click here

Kudos [?]: 932 [4], given: 184

Intern
Intern
User avatar
Joined: 27 Dec 2012
Posts: 6

Kudos [?]: 7 [0], given: 5

Location: Bulgaria
Concentration: Marketing
GMAT Date: 01-30-2013
GPA: 3.5
Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 17 Jan 2013, 03:58
PraPon wrote:
You need LCM of first 7 numbers, NOT factorial. If a number is divisible by 6 then its also divisible by 2 & 3. You dont have to count 2 & 3 again when you consider factor as 6.

\(1=1^1\)
\(2=2^1\)
\(3=3^1\)
\(4=2^2\)
\(5=5^1\)
\(6=2^1 *3^1\)
\(7=7^1\)

\(LCM =1^1 * 2^2 * 3^1 * 5^1 * 7^1= 420\)

Hence choice(A) is the answer.


how about the 4 and the 2? if 4 is divisible by 2 and 2, then should we not consider it as well? I find this confusing.

Kudos [?]: 7 [0], given: 5

Manager
Manager
avatar
Joined: 04 Jan 2013
Posts: 79

Kudos [?]: 17 [0], given: 1

Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 17 Jan 2013, 09:31
the question stem says that the number is divisible by each of the integers from 1 through 7..then,simply,it means that each number is a factor of our lowest common multiple..hence 420 holds water

Posted from my mobile device

Kudos [?]: 17 [0], given: 1

Manager
Manager
User avatar
Joined: 12 Jan 2013
Posts: 218

Kudos [?]: 79 [0], given: 47

GMAT ToolKit User
Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 29 Dec 2013, 11:01
Bunuel wrote:
SOLUTION

What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?

(A) 420
(B) 840
(C) 1,260
(D) 2,520
(E) 5,040

The integer should be divisible by: 2, 3, 4(=2^2), 5, 6(=2*3), and 7. The least common multiple of these integers is LCM=2^2*3*5*7=420.

Answer: A.



Hi Bunuel,

I do understand the LCM but can you explain WHY when we have four sets of 2's we eliminate TWO of them?

For our two 3's, we eliminate one of them and I understand why - we might have the "same" 3. But when we eliminate two 2's, it's not as intuitive to me. Is it simply that, when we have an even number of the same integer, we remove half of them when we calculate the LCM? If so, what would've happened if we had three 2's or five 3's?

Kudos [?]: 79 [0], given: 47

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129095 [0], given: 12194

Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 29 Dec 2013, 11:20
aeglorre wrote:
Bunuel wrote:
SOLUTION

What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?

(A) 420
(B) 840
(C) 1,260
(D) 2,520
(E) 5,040

The integer should be divisible by: 2, 3, 4(=2^2), 5, 6(=2*3), and 7. The least common multiple of these integers is LCM=2^2*3*5*7=420.

Answer: A.



Hi Bunuel,

I do understand the LCM but can you explain WHY when we have four sets of 2's we eliminate TWO of them?

For our two 3's, we eliminate one of them and I understand why - we might have the "same" 3. But when we eliminate two 2's, it's not as intuitive to me. Is it simply that, when we have an even number of the same integer, we remove half of them when we calculate the LCM? If so, what would've happened if we had three 2's or five 3's?


From here: math-number-theory-88376.html

The lowest common multiple or lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple both of a and of b.

To find the LCM, you will need to do prime-factorization. Then multiply all the factors (pick the highest power of the common factors).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 129095 [0], given: 12194

Intern
Intern
avatar
Joined: 12 Aug 2014
Posts: 18

Kudos [?]: [0], given: 72

What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 24 Nov 2014, 13:46
Bunuel wrote:
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?

(A) 420
(B) 840
(C) 1,260
(D) 2,520
(E) 5,040

Practice Questions
Question: 40
Page: 157
Difficulty: 600


With this approach, if LCM of these numbers(from 1 to 7) was not available in options, than precious time could have been wasted while calculating LCM.

So in my opinion the quickest and most accurate approach would be to check the divisibility of each given option (by starting with lowest one) by using following rules:

3>>>>sum of digits should be divisible by 3
6>>>>integer should be divisible by both 2 and 3
9>>>>sum of digits should be divisible by 9
4>>>>should be divisible by 2 twice
5>>>>should be 0 or 5 in the end
7>>>>check divisibility in normal way

Please guide me if i am wrong?

Kudos [?]: [0], given: 72

Intern
Intern
avatar
Joined: 09 Jun 2015
Posts: 6

Kudos [?]: [0], given: 3

Lowest positive integer that is divisible by each... [#permalink]

Show Tags

New post 15 Sep 2015, 13:03
OG 13/2015 - PS - 40 - 157:

What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?

A) 420
B) 840
C) 1260
D) 2520
E) 5040

Seeking a better explanation for the answer and a faster way to solve. In my approach I attempted to figure out if each term was divisible by each 1, 2, 3, 4, 5, 6, and 7, starting with D and B. I see now this was not the right approach. In reviewing the explanation provided from MGMAT, I am still confused and would appreciate clarification on how to solve.

Kudos [?]: [0], given: 3

Expert Post
Math Forum Moderator
avatar
B
Joined: 20 Mar 2014
Posts: 2675

Kudos [?]: 1725 [0], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 15 Sep 2015, 13:11
KOS75 wrote:
OG 13/2015 - PS - 40 - 157:

What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?

A) 420
B) 840
C) 1260
D) 2520
E) 5040

Seeking a better explanation for the answer and a faster way to solve. In my approach I attempted to figure out if each term was divisible by each 1, 2, 3, 4, 5, 6, and 7, starting with D and B. I see now this was not the right approach. In reviewing the explanation provided from MGMAT, I am still confused and would appreciate clarification on how to solve.


Search for a question before posting. Topics merged.

Lowest positive integer = LCM of (1,2,3,4,5,6,7) = LCM (1,2,3,2^2,5,2*3,7) = 1*2^2*3*5*7 = 1*4*3*5*7=420.

For LCM of 2 numbers, you need to break down the numbers to their prime factors and then the LCM will be composed of the product of prime factors raised to the heighest power in either of the 2 numbers.

In the given question, you had 2 as the highest power of 2 and 1 as the highest power of 3,5,7
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1725 [0], given: 792

Expert Post
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 396

Kudos [?]: 336 [0], given: 10

Location: India
GMAT 1: 760 Q50 V44
Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 16 Sep 2015, 05:36
KOS75 wrote:
OG 13/2015 - PS - 40 - 157:

What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?

A) 420
B) 840
C) 1260
D) 2520
E) 5040

Seeking a better explanation for the answer and a faster way to solve. In my approach I attempted to figure out if each term was divisible by each 1, 2, 3, 4, 5, 6, and 7, starting with D and B. I see now this was not the right approach. In reviewing the explanation provided from MGMAT, I am still confused and would appreciate clarification on how to solve.


We simply need to find the LCM of 1,2,3,4,5,6,7 here and that is 420.

LCM of a set of numbers is the product of highest powers of primes numbers in that set.
In this case LCM = 1*2^2*3*5*7 = 420

Moreover, if you are testing options in a question that asks you to find the lowest value, you should always start with the lowest one.
This ways if the answer is the lowest option (as is the case here), yo do not need to look further.
_________________

Reach out to us at bondwithus@gmatify.com

Image

Kudos [?]: 336 [0], given: 10

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1545

Kudos [?]: 837 [0], given: 5

Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 27 May 2016, 07:22
Bunuel wrote:
What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?

(A) 420
(B) 840
(C) 1,260
(D) 2,520
(E) 5,040


We need to determine the smallest number that is divisible by the following:

1, 2, 3, 4, 5, 6, and 7

That is, we need to find the least common multiple of 1, 2, 3, 4, 5, 6, and 7; however, it may be easiest to use the answer choices and the divisibility rules.

Let’s start with answer choice A, 420.

Since 420 is an even number we know 2 divides into 420.

Since the digits of 420 add to 6 (a multiple of 3), we know 3 divides into 420.

Since the last two digits of 420 (20) is divisible by 4, we know 4 divides into 420.

Since 420 ends in a zero, we know 5 divides into 420.

Since 420 is divisibly by both 2 and 3, we know 6 divides into 420.

Finally, we need to determine whether 420 is divisible by 7. While there is no easy divisibility rule for 7, we do know that 7 divides evenly into 42, so it must also divide evenly into 420.

Thus, we have determined that 420 is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive.

The answer is A.
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 837 [0], given: 5

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16605

Kudos [?]: 273 [0], given: 0

Premium Member
Re: What is the lowest positive integer that is divisible by [#permalink]

Show Tags

New post 12 Jun 2017, 16:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

Re: What is the lowest positive integer that is divisible by   [#permalink] 12 Jun 2017, 16:00
Display posts from previous: Sort by

What is the lowest positive integer that is divisible by

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.