If n is the least of 3 consecutive positive integers and : GMAT Problem Solving (PS)
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# If n is the least of 3 consecutive positive integers and

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If n is the least of 3 consecutive positive integers and [#permalink]

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24 Feb 2012, 22:04
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If n is the least of 3 consecutive positive integers and n is odd, what is the least common multiple of the 3 integers, in terms of n?

A. n(n+1)(n+2)
B. n^3 + 3
C. n(n^2 + 2)
D. n^2 + 3
E. 3(n +1)
[Reveal] Spoiler: OA
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Re: PT #8 PS 2 Q 17 [#permalink]

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24 Feb 2012, 23:43
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eybrj2 wrote:
If n is the least of 3 consecutive positive integers and n is odd, what is the least common multiple of the 3 integers, in terms of n?

A. n(n+1)(n+2)
B. n^3 + 3
C. n(n^2 + 2)
D. n^2 + 3
E. 3(n +1)

Two consecutive integers are co-prime, meaning that they do not share any common factor but 1. For example 4 and 5 are consecutive integers and they do not share any common factor but 1. This means that the leas common multiple of two consecutive integers is always their product: LCM(4, 5)=20.

So, for n, n+1 and n+2 each pair consecutive terms is co-prime (n and n+1, as well as n+1 and n+2). Now, since n is odd, then n and n+2 are also co-prime (consecutive odd integers are also co-prime: 3 and 5, 5 and 7, 7 and 9, ...), which means that all 3 integers are co-prime to each other, hence the least common multiple of the 3 integers is n(n+1)(n+2).

Else you can pick some number for n, say 3. Then three consecutive integers will be 3, 4, and 5, their LCM is 3*4*5=60. Now, just plug 3 in the answer choices to see which yields 60: only A.

Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only. For example if you pick n=1 then you get two "correct" choices A and E.

Hope it helps.
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Re: If n is the least of 3 consecutive positive integers and [#permalink]

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27 May 2013, 04:51
Bumping for review and further discussion.
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Re: If n is the least of 3 consecutive positive integers and [#permalink]

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06 Dec 2014, 22:46
Hello from the GMAT Club BumpBot!

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Re: If n is the least of 3 consecutive positive integers and [#permalink]

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29 Feb 2016, 16:39
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).

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Re: If n is the least of 3 consecutive positive integers and [#permalink]

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16 Mar 2016, 09:13
Excellent Question
here i choose N=1 and discarded B,C,D then choose N=3 and Marked A as the option.
Nice One
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Mock Test -1 (Integer Properties Basic Quiz) ---> http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1676182

Mock Test -2 (Integer Properties Advanced Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1765951

Mock Test -2 (Evensand Odds Basic Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1768023

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Re: If n is the least of 3 consecutive positive integers and   [#permalink] 16 Mar 2016, 09:13
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