Question

if two positive integers p and q are written as p= a^2 b^3 and q= a^3 b : a and b are prime no.s, then verify :LCM(p,q) *HCF (p,q) = pq

Answer 1

a^2b Is the HCF and a^3b^3 is the LCM
LCM*HCF=pq
a^3b^3*a^2b=a^2b^3*a^3b
a^5b^4=a^5b^4
Hence proved

Answer 2

Lcm(p,q)*hcf(p,q)=pq
Ans:
Lcm(p,q)=a3b3
Hcf(p,q)=a2b
Lcm(p,q)*hcf(p,q)=a5b4=(a2b3)a3b)=pq.

Hence, verified