Consider integers $m$ and $n$, not both 0. Show that gcd$(m,n)$ is the smallest positive integer that can be written as $am + bn$ for integers $a$ and $b$.
I'm confused on what exactly to do--I'm having trouble wrapping my head around the question. I know that using the euclidean algorithm backwards will provide me with an $a$ and a $b$ such that $am + bn = gcd(m,n)$. But I'm not sure how to prove that it is the smallest positive integer.