Question

If two positive integers p and q are written as p= a²b³ and q= a³b; a, b are prime numbers, then verify: LCM (p, q) × HCF (p, q) = pq

Answer 1

heya


it's too easy .

first of all factorization method apply.


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

a^3b=a*a*a*b=q

lcm (p, q)=a*a*b*a*b*b

lcm(p,q)=a^3b^3

and hcf(p,q)=a*a*b.


hcf (p,q)=a^2b

lcm*hcf=product of their no.

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

a^6*b^4=a^6*b^4
lhs=Rhs

hence here prooved that
product of hcf*lcm=product of their no.

hope it help you


@rajukumar1☺