- #1
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.
Number theory proof - gcf and lcm
- Thread starter roto25
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- Number theory Proof Theory
In summary, the conversation discusses the problem of proving the equality of gcd of the least common multiple of two numbers and a third number, with the least common multiple of the gcd of the two numbers and the gcd of the third number. The suggested solution is to use Venn diagrams to represent the prime factors involved in the lcm and gcd operations. However, it is not clear if the person is familiar with this method.
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.
- #2
I like Serena
Homework Helper
MHB
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roto25 said:
Hi roto!
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?