# Find the LCM and HCF of the following pair of integers and verify that LCM x HCF = product of the 2 numbers

I) 26 and 91

Ans. 26 = 2 x 13

91= 7 x 13

HCF = 13

LCM = 2 x 7 x 13 = 182

Product of the 2 numbers = 26 x 91 = 2366

HCF x LCM = 13 x 182 = 2366

Hence, product of two numbers = HCF x LCM

II) 510 and 92

510 = 2 x 3 x 5 x 17

92 = 2 x 2 x 23

HCF = 2

LCM = 2 x 2 x 3 x 5 x 17 x 23 = 23460

Product of the two numbers = 510 x 92 = 46920

HCF x LCM = 2 x 23460

= 46920

Hence, product of two numbers = HCF x LCM

III) 336 and 54

336 = 2 x 2 x 2 x 2 x 3 x 7

336 = 24 x 3 x 7

54 = 2 x 3 x 3 x 3

54 = 2 x 3³

HCF = 2 x 3 = 6

LCM = 24 x 3³ x 7 = 3024

Product of the two numbers = HCF x LCM

I) 26 and 91

Ans. 26 = 2 x 13

91= 7 x 13

HCF = 13

LCM = 2 x 7 x 13 = 182

Product of the 2 numbers = 26 x 91 = 2366

HCF x LCM = 13 x 182 = 2366

Hence, product of two numbers = HCF x LCM

II) 510 and 92

510 = 2 x 3 x 5 x 17

92 = 2 x 2 x 23

HCF = 2

LCM = 2 x 2 x 3 x 5 x 17 x 23 = 23460

Product of the two numbers = 510 x 92 = 46920

HCF x LCM = 2 x 23460

= 46920

Hence, product of two numbers = HCF x LCM

III) 336 and 54

336 = 2 x 2 x 2 x 2 x 3 x 7

336 = 24 x 3 x 7

54 = 2 x 3 x 3 x 3

54 = 2 x 3³

HCF = 2 x 3 = 6

LCM = 24 x 3³ x 7 = 3024

Product of the two numbers = HCF x LCM