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 (pq)×HCF(pq)=pq

Answer 1

Answer: p=a^2b^3

q=a^3b

Lcm(p,q)=a^3*b^3 (highest power of the common primes)

HCF(p,q)=a^2*b (lowest power of the common primes)

Lcm(pq)* HCF(pq)=pq

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

a^3*b^3a^2*b =a^3*b^3a^2*b

Hence verified.

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