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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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