GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 May 2019, 08:04

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

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

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
What is the lowest positive integer that is divisible by  [#permalink]

Show Tags

New post 11 Sep 2012, 04:43
4
33
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

73% (01:07) correct 27% (01:17) wrong based on 1191 sessions

HideShow timer Statistics

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
Re: What is the lowest positive integer that is divisible by  [#permalink]

Show Tags

New post 11 Sep 2012, 04:43
7
10
Most Helpful Community Reply
Senior Manager
Senior Manager
User avatar
Joined: 27 Jun 2012
Posts: 365
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
Re: What is the lowest positive integer that is divisible by  [#permalink]

Show Tags

New post 13 Jan 2013, 23:43
8
5
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
Finance your Student loan through SoFi and get $100 referral bonus : Click here
General Discussion
Manager
Manager
avatar
Joined: 12 Mar 2012
Posts: 102
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
2
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!
Senior Manager
Senior Manager
avatar
Joined: 06 Aug 2011
Posts: 329
Re: What is the lowest positive integer that is divisible by  [#permalink]

Show Tags

New post 11 Sep 2012, 10:04
1
1
its A..

1*2*3*2*5*7=420...
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !
Intern
Intern
avatar
Status: Life begins at the End of your Comfort Zone
Joined: 31 Jul 2011
Posts: 43
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
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.
Senior Manager
Senior Manager
avatar
B
Joined: 24 Aug 2009
Posts: 461
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
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
Intern
Intern
User avatar
Joined: 27 Dec 2012
Posts: 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.
Manager
Manager
avatar
Joined: 04 Jan 2013
Posts: 69
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
Manager
Manager
User avatar
Joined: 12 Jan 2013
Posts: 145
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?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
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).
_________________
Intern
Intern
avatar
Joined: 12 Aug 2014
Posts: 17
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?
Intern
Intern
avatar
Joined: 09 Jun 2015
Posts: 6
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.
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2626
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
What is the lowest positive integer that is divisible by  [#permalink]

Show Tags

New post 15 Sep 2015, 13:11
1
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
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 388
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.
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: What is the lowest positive integer that is divisible by  [#permalink]

Show Tags

New post 27 May 2016, 07:22
1
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.
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1284
Re: What is the lowest positive integer that is divisible by  [#permalink]

Show Tags

New post 27 Feb 2018, 09:05
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.


Bunuel if you counted total FOUR 2s here ---> 2, 3, 4(=2^2), 5, 6(=2*3), and 7 then why did you count here only TWO 2s ? LCM=2^2*3*5*7=420. :? PLEASE EXPLAIN :)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55266
Re: What is the lowest positive integer that is divisible by  [#permalink]

Show Tags

New post 27 Feb 2018, 10:17
1
dave13 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.


Bunuel if you counted total FOUR 2s here ---> 2, 3, 4(=2^2), 5, 6(=2*3), and 7 then why did you count here only TWO 2s ? LCM=2^2*3*5*7=420. :? PLEASE EXPLAIN :)


Please read the whole thread and follow the links: https://gmatclub.com/forum/what-is-the- ... l#p1311043
_________________
Manager
Manager
avatar
S
Joined: 23 Sep 2016
Posts: 222
Reviews Badge
Re: What is the lowest positive integer that is divisible by  [#permalink]

Show Tags

New post 28 Feb 2018, 01:01
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

IMO A basically this question indirectly asking for LCM(lowest common factor) and if you find LCM then it is 420.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11002
Re: What is the lowest positive integer that is divisible by  [#permalink]

Show Tags

New post 18 Mar 2019, 15:42
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 Club Bot
Re: What is the lowest positive integer that is divisible by   [#permalink] 18 Mar 2019, 15:42
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  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.