Find the LCM and HCF of the following integers by the prime factorization method 8, 9 and 25

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Solution:

We will find the LCM and HCF of the given integers by applying the prime factorization method. 

Prime factorization is a way of expressing a number as a product of its prime factors.

To solve this question, we will follow the steps below:

• To find the LCM and HCF of the given pairs of the integers, first, find the prime factors of the given 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.

(i) 12, 15 and 21

Prime factors of 12 = 2 × 2 × 3 = 2² × 3

Prime factors of 15 = 3 × 5

Prime factors of 21 = 3 × 7

HCF of 12, 15 and 21 = 3

LCM of 12, 15 and 21 = 2² × 3 × 5 × 7 = 420

(ii) 17, 23 and 29

Prime factors of 17 = 17 × 1

Prime factors of 23 = 23 × 1

Prime factors of 29 = 29 × 1

HCF of 17, 23 and 29 = 1

LCM of 17, 23 and 29 = 17 × 23 × 29 = 11339

(iii) 8, 9 and 25

Prime factors of 8 = 2 × 2 × 2 × 1 = 2³ × 1

Prime factors of 9 = 3 × 3 × 1 = 3² × 1

Prime factors of 25 = 5 × 5 × 1 = 5² × 1

HCF of 8, 9 and 25 = 1

LCM of 8 , 9 and 25 = 2 × 2 × 2 × 3 × 3 × 5 × 5 = 1800

☛ Check: NCERT Solutions for Class 10 Maths Chapter 1

Video Solution:

NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.2 Question 3

Summary:

The LCM and HCF of the following integers (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25 by applying the prime factorisation method are (i) 420 and 3, (ii) 11339 and 1 (iii) 1800 and 1 respectively.

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