Question

If two positive integers p and q are written as p= a^2 b^3 and q= a^3 b; a, b are prime numbers, then verify: LCM (p, q) x HCF (p, q) = pq

Answer 1

When we find the LCM and HCF of the following prime numbers p and q,
we get LCM(p,q)=a³b³
and HCF(p,q)=a²b
then using the formula
pq=LCM(p,q)×HCF(p,q)
LHS=> pq
=a²b³×a³b
$= {a}^{5} {b}^{4}$
Now RHS=> LCM(p,q)×HCF(p,q)
=a³b³×a²b
$= {a}^{5} {b}^{4}$

Hence LHS= RHS