Question

If 2 positive integers p and q are written as p=a2b3 and q=a3b;a and b are prime numbers then verify:LCM(p,q) x HCF(p,q)=pq

Answer 1

Given :

p = a^2b^2 and q = q^3b.

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

HCF (p, q) = a^2b

L.H.S = LCM (p, q) × HCF (p, q) = a^5b^4

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

= pq

LCM (p, q) × HCF (p, q) = pq

L.H.S. = R.H.S.

Proved !

Answer 2

Answer:

Step-by-step explanation:

H.C.F.(p,q)=a^2b

L.C.M.(p,q)=a^3b^2

L.C.M.(p,q)×H.C.F.(p,q)=a^5b^3

pq=a^5b^3

Therefore, LCM (p,q)×HCF (p,q)=pq