Exercise 1.1, 3

Find the LCM and HCF of the following integers by applying the prime factorisation method.

(i) 12, 15 and 21

 

Solution:

Prime Factorization

          12 = 2² × 3

          15 = 3 × 5

          21 = 3 × 7

Find HCF

The common factor among all numbers is only 3.

So, HCF = 3.

Find LCM

The LCM is the product of the highest powers of all prime factors:

          LCM = 2² × 3 × 5 × 7 = 420

 

Find the LCM and HCF of the following integers by applying the prime factorisation method.

(ii) 17, 23 and 29

 

Solution:

Prime Factorization

          17 = 17  (Prime number)

          23 = 23 (Prime number)

          29 = 29 (Prime number)

Find HCF

Since all numbers are prime and different, HCF = 1.

Find LCM

The LCM is the product of all numbers:

          LCM = 17 × 23 × 29 = 11339

 

Find the LCM and HCF of the following integers by applying the prime factorisation method.

(iii) 8, 9 and 25

 

Solution:

Prime Factorization

         8 = 2³

         9 = 3²

         25 = 5²

Find HCF

There are no common prime factors among all three numbers, so HCF = 1.

Find LCM

The LCM is the product of the highest powers of all prime factors:

           LCM = 2³ × 3² × 5² = 1800