@amusingminnow These types of problems are tricky -- it's asking that **given \(\frac{\text{lcm}(a,b)}{\gcd(a,b)}=b \)**, which of the options **must** be true. So the only thing we know that's true for sure is that \(\frac{\text{lcm}(a,b)}{\gcd(a,b)}=b \).

We can't just assume that \(a=b^2\), because the problem never told us that! It just so happens that if \(a=b^2\), then the requirements are fulfilled. But, \(a\) doesn't have to be equal to \(b^2\). For example, \(a=9,b=6\) works.

Make sure that when you're doing these problems, start with the given, and then find what must be true using only the given. Using that, you get that the fifth option is the right answer. If you want to look at the thread for the solution you can find it here: https://forum.poshenloh.com/topic/724/confusing-solution/2

Hope this helps!