What is the least common multiple of the positive integer x and 12?

Question

(1) The least common multiple of x and 9 is 45?
(2) The least common multiple of x and 4 is 20?

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What is the LCM of x and 12?

(1) The Least Common Multiple of x and 9 is 45?
(2) The Least Common Multiple of x and 4 is 20?

urshi · Answer

(1) The least common multiple of x and 9 is 45

This means the X can be 45 or 5. So NOT SUFFICIENT.

(2) The least common multiple of x and 4 is 20?
This means the X can be 20 ,10 or 5. LCM( 12, X ) = 60 
So, SUFFICIENT.

Answer : B

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AjitJangale · Answer

1. The LCM of x and 9 is 45

So x can be 5 or 15 or 45.

LCM (5,12) = 60, LCM (15,12) = 60 or LCM (45,12) = 360

So Insufficient.

2. The LCM of x and 4 is 20

So x can be 5 or 10 or 20.

LCM (5,12) = 60, LCM (10,12) = 60 or LCM (20,12) = 60

So sufficient.

IMO Ans is B.

GMATinsight · Answer

Question: LCM (x,12) = ?

Statement 1 : LCM (x,9) = 45

i.e. x can be {5, 15, 45}

i.e. LCM (x,12) can be {60, or 180} hence

NOT SUFFICIENT

Statement 2 : LCM (x,4) = 20

i.e. x can be {5, 10, 20}

i.e. LCM (x,12) can be {60} hence

SUFFICIENT

Answer: Option B

logro · Answer

Statement 1: LCM of x and 9 is 45

x can be 5,15,45

which implies LCM (5,12) = 60, LCM (15,12)= 180 ...

Hence NOT sufficient

Statement 2: LCM of x and 4 is 20

x can be 5,10,20

which implies LCM (5,12)= 60, LCM (10,4)= 60 and LCM (20,4)= 60

Hence Statement 2 alone is Sufficient

OA B

avigutman · Answer

Video solution from Quant Reasoning starts at 0:26 Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=wnRa7dIYm2I

woohoo921 · Answer

@avitgutman,

To clarify, for statement two you originally said that x may or may not have up to two 2s, no 2s at all, or a single 2.

Then, you said you actually need two 2s. Is this is because the question asks for the LCM between x and 12, and you know that twelve has two 2s? So, the two 2s from the 4 and 20 match the two 2s in 12?

bumpbot · Answer

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What is the least common multiple of the positive integer x and 12?

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