Q. 24.4( 393 Votes )

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

product of the two numbers.

(i) 26 and 91

(ii) 510 and 92

(iii) 336 and 54

Answer :

(i) 26 = 2×13


91 = 7×13


HCF =13


LCM = 2×7×13 =182


Product of the two numbers = 26×91 = 2366


HCF×LCM = 13×182 = 2366


Hence, product of two numbers = HCF×LCM


(ii) 510 = 2×3×5×17


92 = 2×2×23


HCF = 2


LCM = 2×2×3×5×17×23 = 23460


Product of the two numbers = 510×92 = 46920


HCF×LCM = 2×23460


HCF×LCM = 46920


Hence, product of two numbers = HCF×LCM


(iii) 336 = 2×2×2×2×3×7


336 = 24×3×7


54 = 2×3×3×3


54 =2×33


HCF = 2×3 = 6


LCM = 24×33×7 = 3024


Product of the two numbers = 336×54 = 18144


HCF×LCM = 6×3024 = 18144


Hence, product of two numbers = HCF×LCM

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