abstract algebra - Greatest common divisor of $X^n-1$ and $X^m-1$

Let $f=X^n-1$ and $g=X^m-1$ be two polynomials. Show that: $$\left(f,g\right)=X^{\left(n,m\right)}-1,$$ where $\left(a,b\right)=$ greatest common divisor of $a$ and $b$.