It is currently 26 Sep 2017, 07:45

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Which of the following is the lowest positive integer that

Author Message
TAGS:

### Hide Tags

Manager
Joined: 18 Oct 2011
Posts: 90

Kudos [?]: 87 [1], given: 0

Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Which of the following is the lowest positive integer that [#permalink]

### Show Tags

10 Jan 2013, 09:38
1
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

69% (01:17) correct 31% (01:10) wrong based on 268 sessions

### HideShow timer Statistics

Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

A. 140
B. 210
C. 1400
D. 2100
E. 3500
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Jan 2013, 16:23, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 87 [1], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41714

Kudos [?]: 125101 [1], given: 12079

Which of the following is the lowest positive integer that [#permalink]

### Show Tags

10 Jan 2013, 16:27
1
KUDOS
Expert's post
4
This post was
BOOKMARKED
sambam wrote:
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

A. 140
B. 210
C. 1400
D. 2100
E. 3500

The first 7 positive multiples of 5 are 5, 10, 15, 20, 25, 30 and 35. The least common multiple of these numbers is 2,100.

Or, a shortcut approach:
Discard 140, 1,400 and 3,500 because they are not divisible by 3.
Discard 210 because it's not divisible by 4.
Only option D remains.
_________________

Kudos [?]: 125101 [1], given: 12079

Intern
Joined: 18 Nov 2011
Posts: 36

Kudos [?]: 15 [0], given: 0

Concentration: Strategy, Marketing
GMAT Date: 06-18-2013
GPA: 3.98
Re: Which of the following is the lowest positive integer that [#permalink]

### Show Tags

10 Jan 2013, 17:58
Bunuel wrote:
sambam wrote:
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

A. 140
B. 210
C. 1400
D. 2100
E. 3500

The first 7 positive multiples of 5 are 5, 10, 15, 20, 25, 30 and 35. The least common multiple of these numbers is 2,100.

Or:
Discard 140, 1,400 and 3,500 because they are not divisible by 3.
Discard 210 because it's not divisible by 4.
Only option D remains.

Why are we looking at divisibility by 3 and 4?

Kudos [?]: 15 [0], given: 0

Intern
Joined: 28 Nov 2012
Posts: 44

Kudos [?]: 59 [0], given: 3

Re: Which of the following is the lowest positive integer that [#permalink]

### Show Tags

10 Jan 2013, 18:33
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

A. 140
B. 210
C. 1400
D. 2100
E. 3500

Take 5,10,15,20,25,30, and 35

You can eliminate A and B right off the bat because 25 doesn't go into 140 or 210. I found it easier to look take a two of the multiples and test their divisibility among the choices. If one doesn't work its wrong so 30 and 35.

C) Wrong not divisible by 30
D) Yes for both check 15 that's the only other obscure multiple
E) Not divisible by 30

Kudos [?]: 59 [0], given: 3

Math Expert
Joined: 02 Sep 2009
Posts: 41714

Kudos [?]: 125101 [1], given: 12079

Re: Which of the following is the lowest positive integer that [#permalink]

### Show Tags

10 Jan 2013, 18:53
1
KUDOS
Expert's post
hitman5532 wrote:
Bunuel wrote:
sambam wrote:
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

A. 140
B. 210
C. 1400
D. 2100
E. 3500

The first 7 positive multiples of 5 are 5, 10, 15, 20, 25, 30 and 35. The least common multiple of these numbers is 2,100.

Or:
Discard 140, 1,400 and 3,500 because they are not divisible by 3.
Discard 210 because it's not divisible by 4.
Only option D remains.

Why are we looking at divisibility by 3 and 4?

The least common multiple of 5, 10, 15, 20, 25, 30 and 35 must be a multiple of 3 since 15 is a multiple of 3 and it must a multiple of 4 since 20 is a multiple of 4.

Hope it's clear.
_________________

Kudos [?]: 125101 [1], given: 12079

Intern
Joined: 18 Nov 2011
Posts: 36

Kudos [?]: 15 [0], given: 0

Concentration: Strategy, Marketing
GMAT Date: 06-18-2013
GPA: 3.98
Re: Which of the following is the lowest positive integer that [#permalink]

### Show Tags

10 Jan 2013, 19:38
I knew I was missing something very simple. Thank you

Kudos [?]: 15 [0], given: 0

Manager
Joined: 04 Oct 2011
Posts: 218

Kudos [?]: 62 [0], given: 44

Location: India
GMAT 1: 440 Q33 V13
GPA: 3
Re: Which of the following is the lowest positive integer that [#permalink]

### Show Tags

10 Jan 2013, 20:25
first 7 positive multiples of 5 are 5, 10, 15, 20, 25, 30 and 35.

5 = 1* 5
10 = 2 * 5
15 = 3 * 5
20 = 4 * 5 = $$2^2 * 5$$
25 = 5 * 5 = $$5 ^ 5$$
30 = 6 * 5= $$2*3*5$$
35 = 7* 5

So, LCM would be 1 * $$2^2$$ * 3 * $$5^5$$ * 7 = 2100

actually i made mistake while computing first after going through Bunuel soln i got above one
_________________

GMAT - Practice, Patience, Persistence
Kudos if u like

Kudos [?]: 62 [0], given: 44

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17658

Kudos [?]: 272 [0], given: 0

Re: Which of the following is the lowest positive integer that [#permalink]

### Show Tags

27 Oct 2014, 07:58
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.
_________________

Kudos [?]: 272 [0], given: 0

Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 610

Kudos [?]: 608 [0], given: 298

Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Fantastic NP : Which of the following is the lowest positive integer t [#permalink]

### Show Tags

10 Jul 2015, 02:10
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?
140
210
1400
2100
3500
_________________

Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Kudos [?]: 608 [0], given: 298

Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 610

Kudos [?]: 608 [0], given: 298

Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: Fantastic NP : Which of the following is the lowest positive integer t [#permalink]

### Show Tags

10 Jul 2015, 02:11
This is quite tough bunuel your input needed.
_________________

Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Kudos [?]: 608 [0], given: 298

Math Expert
Joined: 02 Sep 2009
Posts: 41714

Kudos [?]: 125101 [0], given: 12079

Re: Which of the following is the lowest positive integer that [#permalink]

### Show Tags

10 Jul 2015, 02:14
honchos wrote:
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?
140
210
1400
2100
3500

Merging topics.

Please search before posting and name topics properly. Also, please put A, B, C, D, and E in front of the options. Thank you.
_________________

Kudos [?]: 125101 [0], given: 12079

Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2682

Kudos [?]: 1694 [1], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Which of the following is the lowest positive integer that [#permalink]

### Show Tags

10 Jul 2015, 05:02
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
honchos wrote:
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?
140
210
1400
2100
3500

One way to look at it this :

1st 7 multiples of 5:
5 =1*5
10=2*5
15=3*5
20=4*5=2^2*5
25=5^2
30=2*3*5
35=5*7

Always try to break down the numbers into their corresponding prime factors.

For LCM (least common multiple) take the highest powers of 2,3,5,7 which gives us : 2^2 *3*5^2*7 = 2100. Hence D is the correct answer.
_________________

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
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 [?]: 1694 [1], given: 792

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17658

Kudos [?]: 272 [0], given: 0

Re: Which of the following is the lowest positive integer that [#permalink]

### Show Tags

23 Sep 2016, 18:03
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.
_________________

Kudos [?]: 272 [0], given: 0

Manager
Joined: 23 Dec 2013
Posts: 235

Kudos [?]: 10 [0], given: 20

Re: Which of the following is the lowest positive integer that [#permalink]

### Show Tags

29 May 2017, 15:58
sambam wrote:
Which of the following is the lowest positive integer that is divisible by the first 7 positive integer multiples of 5?

A. 140
B. 210
C. 1400
D. 2100
E. 3500

First write out in a single column the first seven positive multiples of 5:

5
10
15
20
25
30
35

Then in the next column write out their prime factors:

5
2*5
3*5
2^2*5
5^2
2*3*5
7*5

For an integer to be divisible by each of these prime groups, it must have all of these primes at their highest power. So it must have at least 5^2 for instance because 5^2 is 25 and this integer must be divisible by 25.

We can narrow the list down to 5^2*7*2^2*3

100*7*3

100*21 = 2100.

Kudos [?]: 10 [0], given: 20

Re: Which of the following is the lowest positive integer that   [#permalink] 29 May 2017, 15:58
Display posts from previous: Sort by