I have this math problem.
Let $a, b, m$ be any positive integers with $\gcd(a,m)=d$ and $\gcd(b,m)=1$.
i) Show that if $k$ is a common divisor to $ab$ and $m$, then $k$ divides $d$.
ii) Use the result in part i) to conclude that $\gcd(ab, m)=d$.
I'm not 100% sure about how to start this. Can I conclude that if $k\mid ab$, then $k\mid a$? If I can do that, then I can say since $k\mid a$ and $k\mid m$, $k\mid d$.