**Question 2. Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.**

26 and 91 (ii) 510 and 92 (iii) 336 and 54

**Answer:**

**(i)**

26 = 2 x 13

91 =7 x 13

HCF = 13

LCM =2 x 7 x 13 =182

Product of two value 26 x 91 = 2366

Product of HCF and LCM 13 x 182 = 2366

**Hence, product of two numbers = product of HCF × LCM **

**(ii)**

510 = 2 x 3 x 5 x 17

92 =2 x 2 x 23

HCF =2

LCM =2 x 2 x3 x 5 x 17 x 23 = 23460

Product of both values 510x92 = 46920

Product of HCF and LCM 2x23460 =46920

**Hence, product of two numbers = product of HCF × LCM **

**(iii)**

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

54 = 2 x 3 x 3 x 3

HCF = 2 x 3 = 6

LCM = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 =3024

Product of number 336 x 54 =18144

Product of HCF and LCM 6 x 3024 = 18144

**Hence, product of two numbers = product of HCF × LCM **