Why do this problem?
It focuses on factorisation into primes and depends on equating the powers of the prime factors.

Key question
If

p

and

q

are primes and

p^{r} q^{s} = p^{t} q^{u}

what can you say about the powers?

If $p^{r / s}$ is an integer what can you say about $r$ and $s$ ?

Possible extension

Try the problem Factorial Fun