If two positive integers p and q are written as p = a 2 b 3 and q = a 3 b; a, b are prime numbers, then verify:

LCM (p, q) × HCF (p, q) = pq

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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

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