LCM Question -- solving for possible m and n

Question

Could someone please help me with the following question:

Find positive integers m and n such that 9 divides m, 15 divides n, and LCM(m,n) = 330. If this is not possible, give a brief explanation as to why it is impossible.

I wrote that the LCM would be at most 135 since 9 x 15 is 135. Thus, it is not possible to satisfy all 3 conditions. Is this reasoning correct?

Edit: I see that my reasoning is wrong. How do I go about answering this question then?

The information I have: 9*k = m, 15*t = n, m * q = 330, and n * r = 330.

Answer 1

You might have $m > 9$ or $n > 15$; equality is not required.

Note that, since $330$ is even, at least one of $m$ and $n$ must also be even.

This should be enough to get you started.

Answer 2

Your argument is wrong. If $m=9$ and $n=60$, then $\mathrm{lcm}(m,n)=180$. So it is not "at most $135$."