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Question 7 - CBSE Class 10 Sample Paper for 2018 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at March 16, 2023 by

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

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

You can download the question paper here  https://www.teachoo.com/cbse/sample-papers/

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Question 7 - CBSE Class 10 Sample Paper for 2018 Boards - Part 2

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Transcript

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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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.