Is this identity true?
gcd(a, lcm(b,c)) = lcm(gcd(a,b), gcd(a,c))
What have you tried so far?
Have you looked for counter examples or attempted a proof?
Do you have an idea of how to prove/disprove statements like these?
I have already proven it, since the exponents of the all primes of the canonical factorization of a, b and c obeys min(a,max(b,c))=max(min(a,b),min(a,c)).
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