Question

If two positive integers p and q
are written
as p= a²b3 and q= a3 b; a, b are prime numbers,
then verify:
LCM (p,q) X HCF (p, q) = pq​

Answer 1

Answer:

Given p=a2b3 and q=a3b

From LHS-

LCM (p,q)×HCF(p,q)

LCM Of a2b3 and a3b= a3b3

and ,HCF of a2b3 and a3b= a2b

Now, Product of LCM AND HCF:-

a3b3 × a2b = a5b4 .

FROM RHS-

pq= p×q = a2b3 × a3b = a5b4

Hence, LHS=RHS .