Check sibling questions

Let a and b be two positive integers such that a = p 3 q 4 and b = p 2 q 3 , where p and q are prime numbers. If HCF(a,b) = p m q n and

LCM(a,b) = p r q s , then (m + n)(r + s) =

(a) 15   (b) 30  (c) 35  (d) 72

 

This question is similar to Question 7 - CBSE Class 10 Sample Paper for 2018 Boards

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Transcript

Question 1 Let a and b be two positive integers such that a = p3q4 and b = p2q3, where p and q are prime numbers. If HCF(a,b) = pmqn and LCM(a,b) = prqs , then (m + n)(r + s) = (a) 15 (b) 30 (c) 35 (d) 72 Given two numbers a = p3q4 and b = p2q3 Finding HCF a = p3q4 = p × p × p × q × q × q × q b = p2q3 = p × p × q × q × q HCF = p × p × q × q × q HCF = p2q3 Comparing HCF = p2q3 with HCF = pmqn ∴ m = 2, n = 3 Finding LCM LCM = p × p × p × q × q × q × q LCM = p3q4 Comparing LCM = p3q4 with LCM = prqs ∴ r = 3, s = 4 Now, (m + n)(r + s) = (2 + 3) × (3 + 4) = 5 × 7 = 35 So, the correct answer is (c)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.