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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] 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] 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] 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] New post 21 Dec 2012, 04:04
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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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Re: What is the LCM of x and 12?   [#permalink] 21 Dec 2012, 04:04
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