algebra precalculus - How to prove that $gcd(t^n-1,t^m-1)=t^{gcd(n,m)}-1$

Let $t$ be an element in any domain where gcd's exist. Then if $m,n$ are positive integer,prove that: $\gcd(t^n-1,t^m-1)=t^{\gcd(n,m)}-1$