Question

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

Answer 1

Given :

p = a^2b^2 and q = q^3b.

LCM (p, q) = a^3b^3

HCF (p, q) = a^2b

L.H.S = LCM (p, q) × HCF (p, q) = a^5b^4

= (a^2b^3) (a^3b)

= pq

LCM (p, q) × HCF (p, q) = pq

L.H.S. = R.H.S.

Proved !