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# What is the lowest positive integer that is divisible by eac

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Math Expert
Joined: 02 Sep 2009
Posts: 50002
What is the lowest positive integer that is divisible by eac  [#permalink]

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06 May 2012, 06:54
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Difficulty:

5% (low)

Question Stats:

79% (00:58) correct 21% (01:08) wrong based on 176 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/what-is-the- ... 38733.html

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

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30 Oct 2014, 00:23
Bunuel wrote:
sravanth 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

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

LCM of 7! = 7 * 6 * 10 = 420

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

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28 Nov 2015, 15:56
Hi All,

This is a great question to TEST THE ANSWERS on, but you have to pay careful attention to what is asked for: we're asked for the LOWEST integer that is divisible by all of those integers. As such, you should start with Answer A. If "A" is not correct, then you TEST B, and so on. There is a Number Property rule that you can use to help you to avoid some of the 'excess math.'

Any number that is divisible by 6 is ALSO divisible by 2 and 3

So, how long would it take you to determine if 420 is divisible by 7, 5, 4 and 6 (or 3 and 2)?

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

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16 Mar 2016, 10:29
The best approach is to calculate the LCM offcourse .
Also by analysing the options we can see that choice A satisfies all the requirements
Hence A
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Re: What is the lowest positive integer that is divisible by eac  [#permalink]

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15 Oct 2017, 02:01
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

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/what-is-the- ... 38733.html
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Re: What is the lowest positive integer that is divisible by eac &nbs [#permalink] 15 Oct 2017, 02:01
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