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