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Can you prove that if $3 \mid 2a$, then $3 \mid a$, with prime factorization?
The statement goes as following: if $3 \mid 2a$, then $3 \mid a$ and $a$ is an integer. In my approach, I used prime factorization, but is this actually valid? This was my approach:
$$3 \mid 2a \...
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Proving gcd($a,b$)lcm($a,b$) = $|ab|$
Let $a$ and $b$ be two integers. Prove that $$ dm = \left|ab\right| ,$$ where $d = \gcd\left(a,b\right)$ and $m = \operatorname{lcm}\left(a,b\right)$.
So I went about by saying that $a = p_1p_2......
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