Nevermind I've worked it out,

If anyone is interested:

Suppose mn/a. Then there exists an interger q such that mn=qa. Using linear combinations we get hcf(a,m)=ra+sm for some intergers r and s, and hcf(a,n)=ta+bn for some intergers t and b.

Therefore:

Hcf(a,m) x hcf(a,n) = (ra+sm)(ta+bn)

=rt(a^2)+rabn+smta+smnb

=rt(a^2)+rabn+smta+sqab using (mn=qa) from above

=a(rta+rbn+smt+sqb)

So that (hcf(a,m)xhcf(a,n))/a