Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 336 and 54

(i) 26 and 91
Factor of 26 = 2 × 13 × 1
Factor of 91 = 7 × 13 × 1
HCF of 26 and 91 = 13 × 1 = 13
LCM of 26 and 91 = 2 × 7 × 13 = 182
LCM × HCF = 182 × 13 = 2366
26 × 91 = 2366
So, LCM.HCF = product of the two numbers = 26 × 91. Hence proved
(ii) 510 and 92
Factor of 510 = 2 × 3 × 5 × 17 × 1
Factor of 92 = 2 × 2 × 23
HCF of 510 and 92 = 2 × 2 = 2
LCM of 510 and 92 = 2 × 2 × 3 × 5 × 17 × 23 = 23,460
LCM × HCF = 23,460 × 2 = 46,920
510 × 92 = 46,920
So, LCM.HCF = product of the two numbers = 510 × 92. Hence proved
(iii) 336 and 54
Factor of 336 = 2 × 2 × 2 × 2 × 7 × 3 × 1
Factor of 54 = 2 × 3 × 3 × 3
HCF of 336 and 54 = 2 × 3 = 6
LCM of 336 and 54 = 2 × 3 × 2 × 2 × 2 × 7 × 3 × 3 = 3,024
LCM × HCF = 3,024 × 6 = 18,144
336 × 54 = 18,144
So, LCM.HCF = product of the two numbers = 336 × 54. Hence proved.