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If the least common multiple of positive integer m and n is

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If the least common multiple of positive integer m and n is [#permalink] New post 12 Jun 2008, 23:09
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Question Stats:

58% (02:19) correct 43% (01:37) wrong based on 40 sessions
If the least common multiple of positive integer m and n is 120, and m:n=3:4, what is the greatest common factor of m and n?

(A) 3
(B) 5
(C) 6
(D) 10
(E) 12
[Reveal] Spoiler: OA

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Last edited by Bunuel on 20 Oct 2013, 22:12, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: If the least common multiple of a positive integer [#permalink] New post 12 Jun 2008, 23:26
vdhawan1 wrote:
If the least common multiple of a positive integer m and n is 120 and m:n is 3:4 what is the greatest common factor of m and n

3
5
6
10
12

Please provide detailed explanations on how to solve this

many thanks


D for me!
x is the least common factor of m and n
m*n=3x*4x=120*x, so x=10, because x can not be 0!

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Re: If the least common multiple of a positive integer [#permalink] New post 13 Jun 2008, 03:56
sondenso wrote:
D for me!
x is the least common factor of m and n
m*n=3x*4x
I don't get this (where does it come from ?)

sondenso wrote:
3x*4x=120*x

This is just false

sondenso wrote:
=120*x, so x=10, because x can not be 0!

I don't get this either.


Can you explain ?
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Re: If the least common multiple of a positive integer [#permalink] New post 13 Jun 2008, 05:37
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D

fist way:

LCM=120=3*2^3*5

1. LCM contains prime number 5, so m or n or both also contain 5.
2. if m:n=3:4 then only both m and m contain 5. Therefore, GCD is 5 or 10.
3. LCM contains 2^3, but in ratio m:n we have only 4=2^2. So, both m and m contain 2. GCD=10.

second way:

m*n=LCM*GCD - it is a formula.
m*n=3x*4x=120*GCD ---> GCD=x^2/10 ---> only 10 works.

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Re: If the least common multiple of a positive integer [#permalink] New post 13 Jun 2008, 05:45
walker wrote:
D

fist way:

LCM=120=3*2^3*5

1. LCM contains prime number 5, so m or n or both also contain 5.
2. if m:n=3:4 then only both m and m contain 5. Therefore, GCD is 5 or 10.
3. LCM contains 2^3, but in ratio m:n we have only 4=2^2. So, both m and m contain 2. GCD=10.
I like this. Thanks !


walker wrote:
second way:

m*n=LCM*GCD - it is a formula.
m*n=3x*4x=120*GCD ---> GCD=x^2/10 ---> only 10 works.

Thanks for the refresh on the formula, I did not remember.

But why is m*n = 3x*4x ?
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Re: If the least common multiple of a positive integer [#permalink] New post 13 Jun 2008, 05:48
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Oski wrote:
But why is m*n = 3x*4x ?


m:n=3:4 --> m=3x, n=4x where x is an integer (m/n=3x/4x=3/4)

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Re: If the least common multiple of a positive integer [#permalink] New post 13 Jun 2008, 05:53
walker wrote:
Oski wrote:
But why is m*n = 3x*4x ?


m:n=3:4 --> m=3x, n=4x where x is an integer (m/n=3x/4x=3/4)

Yes, sure, but why is this x necessarily the GCD ?

Edit : Okay, I got it. This is because there is no common divisors in 3 and 4... (I guess this should be part of the demonstration ^^)
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Re: If the least common multiple of a positive integer m and n [#permalink] New post 20 Oct 2013, 15:04
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vd wrote:
If the least common multiple of a positive integer m and n is 120 and m:n is 3:4 what is the greatest common factor of m and n

3
5
6
10
12

Please provide detailed explanations on how to solve this

many thanks


I just plugged in numbers for m & n. If the ratio is 3:4, then using 3 & 4 for their values works fine, since we're trying to find the GCF, and not the actual values of m&n,

so

m*n=LCM*GCF

3*4=120*GCF
12=120*GCF
10=GCF

D.
Re: If the least common multiple of a positive integer m and n   [#permalink] 20 Oct 2013, 15:04
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