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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

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.

Answer: D.

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

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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

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.

Answer: D.

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.

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27 Oct 2014, 07:58

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Fantastic NP : Which of the following is the lowest positive integer t [#permalink]

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

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23 Sep 2016, 18:03

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

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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.