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

Question

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

Bunuel · Answer

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Gmatdecoder · Answer

I tried to search this one but could'nt find. Please post a solution to this one as I am in doubt regarding OA

Lucky2783 · Answer

(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

EMPOWERgmatRichC · Answer

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:  E

GMAT assassins aren't born, they're made,
Rich

EgmatQuantExpert · Answer

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

pakasaip · Answer

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

bumpbot · Answer

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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

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