Hi There,

I really don't like Number theory, and i'm terrible with it. Can someone please show me how to prove the following?

$\displaystyle gcd(ac,bd) >= gcd(a,b) * gcd(c,d) $ for all a,b,c,d which are natural numbers.

Also, Is $\displaystyle gcd(ac,bd) = gcd(a,b) * gcd(c,d) $ for all a,b,c,d which are natural numbers? Why?