Question 7
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
Given two numbers
p = a2b3
q = a3b
Finding HCF
p = a2b3 = a a b b b
q = a3b = a a a b
HCF = a a b
HCF = a2b
Finding LCM
LCM = a a a b b b
= a3b3
We need to verify
HCF LCM = pq
Since LHS = RHS
Hence proved
Taking LHS
HCF LCM
= a2b a3b3
= a2+3 b1+3
= a5b4
Taking LHS
pq
= a2b3 a3b
= a2+3 b3+1
= a5b4

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.