GCD of multiple elements in a UFD

Question

Suppose that the GCD of $a_1,..,a_r$ is a unit. Show that the GCD of $ka_1,..,ka_r$ is $k$, where $k\in R$.

Its seems simple enough but I can't seem to show that any divisor of $ka_1,..,ka_r$ can divide $k$, i.e. i tried to show the (k) was the smallest principal ideal that contains $ka_1,..,ka_r$.

Answer 1

The $r=2$ case follows from a theorem dealt with here; induction (or extending the methodology there) will help with the general case.