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If a and b are positive even integers, and the least common

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If a and b are positive even integers, and the least common [#permalink] New post 11 Oct 2005, 17:32
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48% (02:22) correct 52% (01:19) wrong based on 132 sessions
If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/n, which of the following statements could be false?

A. n is a factor of both a and b
B. (a*b)/n < ab
C. ab is multiple of 2.
D. (a*b)/n is a multiple of 2.
E. n is a multiple of 4.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 28 Aug 2013, 03:21, edited 1 time in total.
Renamed the topic and edited the question.
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 [#permalink] New post 11 Oct 2005, 18:08
E may be false.
If a=4, b=2 least comm. multiple is 4.
ab/n=4 => n=2 which is not a multiple of 4
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Re: This one from Kaplan.... If 'a' and 'b' are positive even [#permalink] New post 28 Aug 2013, 03:12
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vikramm wrote:
This one from Kaplan....

If 'a' and 'b' are positive even integers, and the least common multiple of 'a' and 'b' is expressed as ab/n, which of the following could be false?
A) n is a factor of both a and b
B) ab/n < ab
C) ab is a multiple of 2
D) ab/n is a multiple of 2
E) n is a multiple of 4


This question is easier if you know that, for any positive integers a and b:

LCM(a,b) * GCD(a,b) = a*b

So LCM(a,b) = ab/GCD(a,b)

In this question, n is just the GCD of a and b. So we know automatically that n is a factor of a and b... A) must be true.
If a and b are both even, they are both divisible by 2, so the smallest possible value for their GCD is 2. That is, n >= 2, so B) must be true
If a and b are even, ab is clearly even, and so is the LCM of a and b, so C) and D) must be true.
E) is the only one that might be false; E will only be true if both a and b are divisible by 4.

hence E
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Re: This one from Kaplan.... If 'a' and 'b' are positive even [#permalink] New post 19 Jan 2014, 06:40
blueseas wrote:
vikramm wrote:
This one from Kaplan....

If 'a' and 'b' are positive even integers, and the least common multiple of 'a' and 'b' is expressed as ab/n, which of the following could be false?
A) n is a factor of both a and b
B) ab/n < ab
C) ab is a multiple of 2
D) ab/n is a multiple of 2
E) n is a multiple of 4



E) is the only one that might be false; E will only be true if both a and b are divisible by 4.

hence E


Any information is provided such that a and b cannot be a multiple of 4 ( 'a' and 'b' are positive even integers - a can be 4 and b can be 16 or 8) ? I don't think it is valid question.
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Re: This one from Kaplan.... If 'a' and 'b' are positive even   [#permalink] 19 Jan 2014, 06:40
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If a and b are positive even integers, and the least common

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