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

(i) 26 = 2×13

91 = 7×13

HCF =13

LCM = 2×17×13 =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