Hi all, have a couple of gcd proofs that I'm stuck with.

1=If gcd(a,c)=1 and gcd(b,c)=1 then gcd(ab,c)=1

thus far all I can figure is to do the following linear combos:

1- ax+cy=1

2-bu+cv=1

3-abz+ct=1

But then I don't know what to do. I try solving for c in one of them and then substituting, but this leads nowhere.

2- If a|c and b|c and gcd(a,b)=1 then ab|c.

This is similar to 1, so I'm also stuck with this one.

Any help would be appreciated. Thanks!