Question

Let a and b be two positive integers such that a=p³q⁴ and b=p²q³, where p and q are prime numbers. If HCF(a,b)=pmqn and LCM(a,b)=prqs, then determine the value of (m+n)(r+s).

(a) 15
(b) 30
(c) 35
(d) 72