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LCM and GCD

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by vittalgmat » Wed Dec 16, 2009 8:26 pm
The least common multiplier of A and B is 120, the ratio of A and B is 3:4, what is the largest common divisor?

How do u attack this problem? .. what are the approaches to take.

[spoiler]OA: 10

We know that A * B = LCM * GCD and we now LCM = 120.
So we get A *B = 120* GCD.
Now how does the ratio of the two numbers play out.
Pls explain in detail

[/spoiler]
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by hamxa » Mon Jan 04, 2010 8:05 am
I will approach this in a different way:

factors of 120 = 2*2*2*3*5

now ratio of A and B is 3:4.
WHICH MEANS A=multiple of 3
and B = multiple of 4

Now: multiple of both has to be the same as its a ratio.
In 120 if we take out 3 and 4, we are left with the factors 2 & 5.

hence A and B should have 2 & 5 in them
A=3*10 =30
B=4*10 = 40

now GCD of 30 & 40 = piece of cake :)
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