# A question regarding primes and least common multiples

Let $$p$$ and $$q$$ be distinct primes. Show that the equation $$\textrm{lcm}(a, b) = (p^2) q$$ has fifteen solutions in positive integers $$a, b$$.

Thanks for any help in advance as I don't know how to proceed with this question.

• Hello, and welcome to MSE. To help get people to answer your question, plus avoid down-voting and getting your question closed, please tell us what you've tried so far, including anything you've had difficulty with. Thanks. – John Omielan Feb 18 at 3:34
• Also, please use MathJax – J. W. Tanner Feb 18 at 3:44
• I can add MathJax for you, seeing that you're new. But I can't add what you've tried so far since I don't know what that is. – Robert Soupe Feb 18 at 4:29

Hint: What are the divisors of $$p^2 q$$?