The first option

Let a=b^2 and b=b, then the LCM = b^2 and the GCD = b.
This means that LCM/GCD=b, which fulfills the requirements.
Why did you mark this as wrong? 
@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/confusingsolution/2
Hope this helps!