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) × HCF (p, q) = pq

### Answer

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

HCF (p, q) = a^{2}b

LCM (p, q) × HCF (p, q) = a^{5}b^{4}

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

= pq