# 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

**Solution:**

LCM × HCF = Product of the two numbers.

- To find the LCM and HCF of the given pairs of the integers, first, find the prime factors of the given pairs of numbers.
- Then, find the product of the smallest power of each common factor in the numbers. This will be the LCM.
- Then, find the product of the greatest power of each prime factor in the number. This would be the HCF.
- Now, you have to verify LCM × HCF = product of the two numbers, find the product of LCM and HCF, and also the two given numbers. If LHS is equal to the RHS then it will be verified.

(i) 26 and 91

Prime factors of 26 = 2 × 13

Prime factors of 91 = 7 × 13

HCF of 26 and 91 = 13

LCM of 26 and 91 = 2 × 7 × 13

= 14 × 17

= 182

Product of these two numbers = 26 × 91

= 2366

LCM x HCF = 182 ×13

= 2366

Product of two numbers = LCM × HCF

(ii) 510 and 92

Prime factors of 510 = 2 × 3 × 5 × 17

Prime factors of 92 = 2 × 2 × 23

HCF of two numbers = 2

LCM of two numbers = 2 × 2 × 3 × 5 × 17 × 23

= 23460

Product of these two numbers = 510 × 92

= 46920

LCM x HCF = 2 × 23460

= 46920

Product of two numbers = LCM × HCF

(iii) 336 and 54

Prime factors of 336 = 2 × 2 × 2 × 2 × 3 × 7

Prime factors of 54 = 2 × 3 × 3 × 3

HCF of two numbers = 6

LCM of two numbers = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 7

= 2^{4} × 3^{3 }× 7

= 3024

Product of these two numbers = 336 × 54

= 18144

LCM x HCF = 3024 × 6

= 18144

Product of two numbers = LCM × HCF

**Video Solution:**

## 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

### NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.2 Question 2 - Chapter 1 Exercise 1.2 Question 2:

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

The LCM and HCF of i) 26 and 91, ii) 510 and 92 and iii) 336 and 54 are: i) 13 and 182, ii) 2 and 23460 and iii) 6 and 3024 respectively.