Question

if two positive integers a and b are written as a=p^2q^3 and b=p^3q, p, q are prime numbers then verify LCM(a.b)*HCF(a,b)=ab

Answer 1

actually, a= p^(2q*3) ⇒ ) ⇒

             

therefore, LCM= p^(6q)

                 HCF= p^(3q)

⇒hcf*lcm = p^9

and a*b =  p^9

hence proved

Answer 2

, a= p^(2q*3) ⇒ ) ⇒

therefore, LCM= p^(6q)

HCF= p^(3q)

⇒hcf*lcm = p^9

and a*b = p^9

hence proved