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

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Bunuel
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What is the least common multiple of the positive integer x and 12? [#permalink] New post   24 Aug 2020, 21:44
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What is the least common multiple of the positive integer 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?



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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?



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B
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Re: What is the least common multiple of the positive integer x and 12? [#permalink] New post   Updated on: 24 Aug 2020, 23:48
(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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Originally posted by urshi on 24 Aug 2020, 21:49.
Last edited by urshi on 24 Aug 2020, 23:48, edited 1 time in total.
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Re: What is the least common multiple of the positive integer x and 12? [#permalink] New post   24 Aug 2020, 23:05
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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.
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Re: What is the least common multiple of the positive integer x and 12? [#permalink] New post   24 Aug 2020, 23:41
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Bunuel wrote:
What is the least common multiple of the positive integer 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?


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

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Re: What is the least common multiple of the positive integer x and 12? [#permalink] New post   25 Aug 2020, 04:32
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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
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Re: What is the least common multiple of the positive integer x and 12? [#permalink] New post   13 Mar 2021, 18:37
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Video solution from Quant Reasoning starts at 0:26
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: What is the least common multiple of the positive integer x and 12? [#permalink] New post   15 Oct 2022, 17:33
avigutman wrote:
Video solution from Quant Reasoning starts at 0:26
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1


@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?
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Re: What is the least common multiple of the positive integer x and 12? [#permalink] New post   25 Nov 2023, 13:36
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Re: What is the least common multiple of the positive integer x and 12? [#permalink]
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