Which of the following could be the least common multiple of two disti

Question

Which of the following could be the least common multiple of two distinct positive integers x and y, where x > y ?

A) 1
B) x-y
C) x
D) y-x
E) y

BrentGMATPrepNow · Accepted Answer

Key Concept #1: All multiples of k are greater than or equal to k  
For example, the multiples of 11 are 11, 22, 33, 44, etc

Key Concept #2: If k and j are positive integers and k > j, the least common multiple of j and k must be greater than or equal to k

So, for this question, the least common multiple of x and y must be greater than or equal to x. 
Only answer choice C is greater than or equal to x

Answer: C

Cheers, 
Brent

rajatchopra1994 · Answer

Explanation:

As, x and y are distinct positive integers, LCM cannot be 1.
As given ; x > y > 0, 
the lowest possible value is x. 
Let, x = 4; y = 2. so, LCM will be = 4

IMO-C

kovid231 · Answer

Since the question said, which of these  could  be. I found it easy to do set cases of LCMs. E.g. 
Let x: 8, y:4.

LCM (4,8): 8.

Which is X. Hence chose option C

TasnimZR · Answer

Here x>y
Assume that, x=3 and y=2
Or, x=4 and y=2

LCM of 3,2 =6 (xy)
 LCM of 4,2=4 (x)
The question is what could be the LCM of x and y.
xy is not in the options. So, it’s x.

Posted from my mobile device

errorlogger · Answer

IanStewart ,  BrentGMATPrepNow 
I find this question to be flawed. This should be a MUST be true q and not COULD be true!
For example x = 6, y = 3
B & C both satisfy the condtions.

Your thoughts?

IanStewart · Answer

If x = 6 and y = 3, then x - y = 3, which is not the LCM of 6 and 3, so x-y is not the LCM of x and y in your example.

If x > y >0, the LCM of x and y must be at least as big as x, so it's impossible for x-y to be the LCM here, because x - y < x.

juliansorre · Answer

We are asked to find a possible value for the LCM (x,y), where x and y are positive integers and x> y

We know that LCM (x,y) must be greater than or equal to the greatest integer among x and y. 
Thus,
LCM(x,y) >= x (1)
From the information given, we also know that x >=1 and y >=1 (positive integers) and that x> y. 
So,
 x>= 2 (2)

From (1) and (2) we can eliminate all alternatives, but C.

Which of the following could be the least common multiple of two disti

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GMAT Problem Solving (PS) Questions

Which of the following could be the least common multiple of two disti

Prep Toolkit

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