Numbers (C10)

If two positive integers p and q are written as p = a2b3 and q = a3b; a, b are prime numbers, then verify:
LCM (p, q) × HCF (p, q) = pq

Answer

LCM (p, q) = a3b3

HCF (p, q) = a2b

LCM (p, q) × HCF (p, q) = a5b4

= (a2b3) (a3b)

= pq