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What is the LCM of x and 12?

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What is the LCM of x and 12?  [#permalink]

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New post 20 Dec 2012, 23:16
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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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Re: What is the LCM of x and 12?  [#permalink]

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New post 21 Dec 2012, 01:11
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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?


(1)
Prime factors of 9 = 3X3; Prime factors of x = a.b.c...(say)
Prime factors of 45 = 5X3X3
So x = {5, 15, 45}
LCM of x and 12 = {60, 60, 180}
Hence INSUFFICIENT

(2)
Prime factors of 4 = 2X2; Prime factors of x = u.v.w...(say)
Prime factors of 20 = 5X2X2
So x = {5, 10, 20}
LCM of x and 12 = {60, 60, 60}, i.e. 60
Hence SUFFICIENT

Since (2) by itself is sufficient, hence (B) is the correct answer.

Thanks for sharing. :)
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Re: What is the LCM of x and 12?  [#permalink]

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New post 21 Dec 2012, 02:03
Zenverse wrote:
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?


(1)
Prime factors of 9 = 3X3; Prime factors of x = a.b.c...(say)
Prime factors of 45 = 5X3X3
So x = {5, 15, 45}
LCM of x and 12 = {60, 60, 180}
Hence INSUFFICIENT

(2)
Prime factors of 4 = 2X2; Prime factors of x = u.v.w...(say)
Prime factors of 20 = 5X2X2
So x = {5, 10, 20}
LCM of x and 12 = {60, 60, 60}, i.e. 60
Hence SUFFICIENT

Since (2) by itself is sufficient, hence (B) is the correct answer.

Thanks for sharing. :)


Thanks to you as well for the reply..
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Re: What is the LCM of x and 12?  [#permalink]

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New post 21 Dec 2012, 04:04
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Ans:

from 1st statement x could be 5,15,45 so l.c.m of (5,12)=60 l.c.m(15,12)=60 and l.c.m(45,12)=180 not sufficient. From 2nd statement x could be 5,10,20 so l.c.m(5,12)=60 l.c.m(10,12)=60 l.c.m(20,12)=60 , the answer is (B). :)
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What is the LCM of x and 12?  [#permalink]

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New post 02 Jul 2019, 10:52
Drik wrote:
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?


What is the theory behind this kind of question? I don't understand the number picking here. Would you please show me other number picking? Bunuel
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What is the LCM of x and 12?  [#permalink]

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New post 02 Jul 2019, 11:38
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RashedVai Hello, I can help.This question is testing your knowledge of number properties, LCM to be specific. The LCM tells us the unique prime factors shared by a set of numbers.

Since we are asked to find the LCM of x and 12, we know 12 = \(2^{2}\) x \(3\), so we need to find x
St 1: LCM(x,9) = 45
45 = \(3^{2}\) x \(5\)
9 = \(3^{2}\), therefore x could be 5, 15 (\(3\) x \(5\)) or even 45 (important to note: the LCM of a factor and its multiple = multiple).
You will get different answers for LCM(x,12) when you test these numbers, therefore statement one is insufficient
St 2: LCM(x,4) = 20
20 = \(2^{2}\) x \(5\)
4 = \(2^{2}\), therefore x could be 5, 10 (\(2\) x \(5\)) or 20 (recall the note above?). Test these numbers for LCM(x,12) and you will get a unique value (60) every time, therefore statement 2 is sufficient and the right answer is B.

Hope this helps. Feel free to reach out if you still have doubts.

Cheers!
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What is the LCM of x and 12?   [#permalink] 02 Jul 2019, 11:38
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