Q. 13.8( 21 Votes )

Find the LCM and HCF of the following pairs of integers and verify that LMC × HCF = Product of the integers:

(i) 26 and 91

(ii) 510 and 92

(iii) 336 and 54

Answer :

(i) Prime factors of 26 = 2 × 13


Prime factors of 91 = 7 ×13


Hence LCM of 26 and 91 = 2 × 7 × 13 = 182


HCF of 26 and 91 is = 13


LCM × HCF = 182 × 13 = 2366


Product of two numbers = 26 × 91 = 2366


Hence from above result we got LCM × HCF = Product of the numbers


(ii) Prime factors of 510 = 2 × 3 × 5 × 17


Prime factors of 92 = 2 × 2 × 13


Hence LCM of 92 and 510 = 2 × 2 × 3 × 5 × 17 × 23 = 23460


HCF of 92 and 510 is = 2


LCM × HCF = 23460 × 2 = 46920


Product of two numbers = 92×510 = 46920


Hence from above result we got LCM × HCF = Product of the numbers


(iii) Prime factors of 336 = 2 × 2 × 2 × 2 × 3 × 7


Prime factors of 54 = 2 × 3 × 3 × 3


Hence LCM of 336 and 54 = 2 × 2 × 2 × 2 × 3 × 3 × 7 = 3024


HCF of 54 and 336 is = 2 × 3 = 6


LCM × HCF = 3024 × 6 = 18144


Product of two numbers = 336 × 54 = 18144


Hence from above result we got LCM × HCF = Product of the numbers


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