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Which of the following CANNOT be the least common multiple of two posi

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Which of the following CANNOT be the least common multiple of two posi  [#permalink]

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New post Updated on: 23 May 2015, 08:23
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Which of the following CANNOT be the least common multiple of two positive integers x and y?

(A) 1
(B) x
(C) y
(D) xy/2
(E) 2xy

Originally posted by Gmatdecoder on 23 May 2015, 08:17.
Last edited by Bunuel on 23 May 2015, 08:23, edited 1 time in total.
Edited the question.
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Re: Which of the following CANNOT be the least common multiple of two posi  [#permalink]

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New post 23 May 2015, 08:25
Gmatdecoder wrote:
Which of the following CANNOT be the least common multiple of two positive integers x and y?

(A) 1
(B) x
(C) y
(D) xy/2
(E) 2xy


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Re: Which of the following CANNOT be the least common multiple of two posi  [#permalink]

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New post 23 May 2015, 08:29
I tried to search this one but could'nt find. Please post a solution to this one as I am in doubt regarding OA
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Which of the following CANNOT be the least common multiple of two posi  [#permalink]

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New post 23 May 2015, 09:58
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Gmatdecoder wrote:
Which of the following CANNOT be the least common multiple of two positive integers x and y?

(A) 1
(B) x
(C) y
(D) xy/2
(E) 2xy



(A) 1 if x=y=1 , LCM=1
(B) x if x=k*y where k is a integer, then lcm(x,y) = x
(C) y if y=k*x where k is a integer, then lcm(x,y) = y
(D) xy/2 if x=\(2*P_1\) and y=\(2*P_2\) where \(P_1 , P_2\) are prime numbers, then LCM(x,y) = \(2*P_1*P_2\) = \(\frac{X*Y}{2}\)
(E) 2xy well, the answer for this question was this option straightforward . if there is something common between x and y then that would have been LCM but if there is nothing common between x and y , then the first multiple of X and Y will be \(X*Y\) and not \(2*X*Y\)
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Re: Which of the following CANNOT be the least common multiple of two posi  [#permalink]

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New post 23 May 2015, 11:37
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Hi Gmatdecoder,

You can approach this question by TESTing VALUES and eliminating answer choices...

We're told that X and Y are POSITIVE INTEGERS. We're asked which of the answer choices CANNOT be the least common multiple (LCM) of X and Y?

IF....
X = Y = 1
the LCM = 1
Eliminate Answer A

IF....
X = 2, Y = 1
The LCM = 2 = X
Eliminate Answer B

IF....
X = 1, Y = 2
The LCM = 2 = Y
Eliminate Answer C

IF....
X = Y = 2
the LCM = 2
Eliminate Answer D

There's only one answer left....

Final Answer:

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Re: Which of the following CANNOT be the least common multiple of two posi  [#permalink]

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New post 23 May 2015, 21:32
2
Hi Gmatdecoder,

This question could have been easily solved had you been mindful of the constraints on values of LCM. Take note of the range of values of LCM of a set of numbers:

Magnitude of the largest integer of the set <= LCM of a set of integers<= Product of magnitude of all integers in the set

As you would see here that LCM of two numbers x and y can take maximum value of xy. Hence anything greater than xy will not be the possible value of LCM i.e. LCM(x, y) can't take a value of 2xy.

Want to know how is this range calculated and other such important points on LCM-GCD, go through our article 3 Deadly Mistakes you must avoid in LCM-GCD questions

Hope this helps :)

Regards
Harsh
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Re: Which of the following CANNOT be the least common multiple of two posi  [#permalink]

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New post 12 Nov 2016, 02:21
Gmatdecoder wrote:
Which of the following CANNOT be the least common multiple of two positive integers x and y?

(A) 1
(B) x
(C) y
(D) xy/2
(E) 2xy


if GMAT mentions 2 variables, x and y, is it always possible that they can be the same integer (x=y).
In this question, I think that x and y must be 2 different integers, so I eliminated choice A
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Re: Which of the following CANNOT be the least common multiple of two posi  [#permalink]

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