Number theory proof - gcf and lcm

roto25
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Homework Statement


Prove gcd(lcm(a, b), c) = lcm(gcd(a, c), gcd(b, c))

I've tried coming up with a way to even rewrite it but I'm not really able to do it.
 
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roto25 said:

Homework Statement


Prove gcd(lcm(a, b), c) = lcm(gcd(a, c), gcd(b, c))

I've tried coming up with a way to even rewrite it but I'm not really able to do it.

Hi roto! :smile:

Easiest is to set up a couple of Venn diagrams with the supposed prime factors in it.
An lcm is a union and a gcd is an intersection.

Do you know how to do that?
 

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