Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of two numbers. (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54

Question Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of two numbers.
Board CBSE
Textbook NCERT
Class  Class 10
Subject Maths
Chapter  Chapter 1 Real Numbers

Question – Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of two numbers.
(i) 26 and 91
(ii) 510 and 92    
(iii) 336 and 54

Solution:

We know that the HCF of two numbers is equal to the product of the smallest power of each common prime factor in the numbers.
And LCM of two numbers equal to the product of the greatest power of each prime factor, involved in the numbers.

(i) 26 and 91

26 = 2 × 13

91 = 7 × 13

Here 13 is common in both the prime factors of 26 and 91.

HCF of 26 and 91 is 13

LCM of these two numbers = 2 × 7 × 13 =182.

HCF × LCM = 13 × 182 = 2366

Product of 26 and 91 = 26 × 91 = 2366.

Hence, LCM × HCF = Product of the given two numbers

(ii) 510 and 92

510 = 2 × 3 × 5 × 17

92 = 2 × 2 × 23

Here, 2 is common in both the prime factors of 510 and 92

HCF of 510 and 92 is 2

LCM = 2 × 2 × 3 × 5  17 × 23 = 23460

HCF × LCM = 2 × 23460 = 46920

Product of 510 and 92 is = 510 × 92 = 46920.

Hence, LCM × HCF = Product of the given two numbers

(iii) 336 and 54

336 = 2 × 2 × 2 × 2 × 3 × 7

54 = 2 × 3 × 3 × 3

Here, 2 and 3 are common prime factors of 336 and 54.

HCF = 2×3 = 6

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 7 = 3024

HCF × LCM = 6 × 3024 = 18144

Product of336 and 54 = 336 × 54 = 18144

Hence, LCM × HCF = product of the given two numbers

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