Let $m, n ∈\Bbb Z$ be nonzero integers, $d = \gcd(m, n)$ and $L = \operatorname{lcm}(m, n)$. Show that $dL = mn$.

Asked Aug 23 '20 at 21:13

Active Aug 23 '20 at 21:52

Viewed 137 times

I just need help starting this proof. I know what the definition of gcd and lcm mean in a formula sense, but I think I'm missing something.

edited Aug 23 '20 at 21:22

Bernard

asked Aug 23 '20 at 21:13

HSteve16

2
This has got got be a repeat; please search the site, because I’m sure it’s been covered before. 2. “the proof” depends on what you know or what you want to use. One can prove it using unique factorization into primes, or using the universal properties of the gcd and the lcm, or other ways. You need to give context for your question, specifically what you are expected to use to prove it, or what you want to use to prove it, what related results you know, etc.

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