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# Which of the following is the lowest positive integer that

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Which of the following is the lowest positive integer that [#permalink]  10 Jan 2013, 08:38
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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, 15:23, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Which of the following is the lowest positive integer that [#permalink]  10 Jan 2013, 15:27
Expert's post
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.
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Re: Which of the following is the lowest positive integer that [#permalink]  10 Jan 2013, 16:58
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?
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Re: Which of the following is the lowest positive integer that [#permalink]  10 Jan 2013, 17:33
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
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Re: Which of the following is the lowest positive integer that [#permalink]  10 Jan 2013, 17:53
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.
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Re: Which of the following is the lowest positive integer that [#permalink]  10 Jan 2013, 18:38
I knew I was missing something very simple. Thank you
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Re: Which of the following is the lowest positive integer that [#permalink]  10 Jan 2013, 19:25
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
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Re: Which of the following is the lowest positive integer that [#permalink]  27 Oct 2014, 06:58
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Re: Which of the following is the lowest positive integer that   [#permalink] 27 Oct 2014, 06:58
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