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GCF / LCM DS Problem

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by mlaboda » Sun Nov 22, 2009 6:34 pm
Thank you for helping me understand this problem!

If x and y are positive integers, what is the value of xy?

1. The greatest common factor of x and y is 10.
2. The least common multiple of x and y is 180.

Ans. B
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by RoadtoIVY » Sun Nov 22, 2009 8:28 pm
For any two positive integers x and y:

xy = (GCF of x and y) X (LCM of x and y)
In this case, it would be 10 X 180 = 1800
so C is the answer.
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by heshamelaziry » Sun Nov 22, 2009 9:28 pm
RoadtoIVY wrote:For any two positive integers x and y:

xy = (GCF of x and y) X (LCM of x and y)
In this case, it would be 10 X 180 = 1800
so C is the answer.

But mlaboda says OA is B
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by RoadtoIVY » Sun Nov 22, 2009 9:34 pm
That is incorrect. Please refer to this page:
https://www.manhattangmat.com/forums/if- ... -t282.html
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by mlaboda » Mon Nov 23, 2009 8:37 am
C is the correct answer. My original post was wrong. Thanks for keeping me honest!
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by heshamelaziry » Mon Nov 23, 2009 10:14 am
RoadtoIVY wrote:For any two positive integers x and y:

xy = (GCF of x and y) X (LCM of x and y)
In this case, it would be 10 X 180 = 1800
so C is the answer.

Where this rule come from? could you please explain this rule by a simple example of two integers?
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by palvarez » Wed Nov 25, 2009 2:40 pm
heshamelaziry wrote:
RoadtoIVY wrote:For any two positive integers x and y:

xy = (GCF of x and y) X (LCM of x and y)
In this case, it would be 10 X 180 = 1800
so C is the answer.

Where this rule come from? could you please explain this rule by a simple example of two integers?
it is a simple proof, but hard to type here. Check here

https://books.google.com/books?id=KJwvt2 ... ax&f=false
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