DO NOT FEAR! I emailed my maths teacher, and within a couple hours i got this response.

'If you use a venn diagram or otherwise remove common factors then you get p = 2 x 3 (to the power k) x 5, q = 2 (to the power k)x3x5. Common factors are 2, 3 and 5 so remove each of these once from pxq so 5 x 3(to the power k)x 2(to the power k)= 180 then 5 x 6 (to the power k) = 180, divide by 5, therefore 6 (to the power k) = 36, hence k = 2 . I hope that helps.'

A simply divine and yet complex answer to what would seem a very, very confusing question. With k being 2 from a simple venn diagram, who would've thought?

This leaves the answer as, P=2x2x3x5=60, and Q=2x3x3x5=90, K=2. Guess we were over complicating it :L