Show that the map $\mathbb{Z}_n^*\to \mathbb{Z}_m^*$ is surjective Let $m,n \in \mathbb{Z}$ such that $m|n$. Show that the map $$f: \mathbb{Z}_n^*\to \mathbb{Z}_m^*$$ $$f({a \pmod n}) = (a \pmod m)$$ is surjective. I am not able to figure out any simple way to tackle this... Any hints? 

This should be a comment, but I had trouble with formatting in the comments. 
Evidently, the same proof will work for $R/I \to R/J$ where $R$ is a PID.  The more general problem was considered 
here and
here.   
A nice generalization is that a surjection $f: R \to S$, where the rings are commutative Artinian, maps units onto units.
