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, we have to verify LCM × HCF = product of the two numbers.

(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 × 13

= 182

Product of these two numbers = 26 × 91

= 2366

LCM × HCF = 182 × 13

= 2366

Thus, the 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 the two numbers = 2

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

= 23460

Product of these two numbers = 510 × 92

= 46920

LCM x HCF = 2 × 23460

= 46920

Thus, the 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 the two numbers = 6

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

= 2⁴ × 3³ × 7

= 3024

Product of these two numbers = 336 × 54

= 18144

LCM x HCF = 3024 × 6

= 18144

Thus, the product of two numbers = LCM × HCF

☛ Check: NCERT Solutions for Class 10 Maths Chapter 1

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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

Summary:

The LCM and HCF of the following pairs of integers 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 and we have verified that LCM × HCF = product of the two numbers in each case.

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