We want to show that there exist divisors $c$ of $a$ and $d$ of $b$ such that $(c, d) = 1$ and $cd = [a, b]$, where $[a, b]$ denotes the least common multiple of $a$ and $b$.
We know that $ab = (a, b)[a, b]$, where $(a, b)$ is the greatest common divisor of $a$
Show more…