Question

how to find HCF and LCF in factorisation method ​

Answer 1

LCM by Prime Factorization Method:-

Here given natural numbers are written as the product of prime factors. The lowest common multiple will be the product of the all prime factors with the highest degree (power).

Example 1:

Find the LCM of 20 and 12 by prime factorization method.

Solution:

Step 1: To find LCM of 20 and 12 write each number as a product of prime factors. 20=2×2×5=22×512=2×2×3=22×3

Step 2: Multiply all the prime factors with the highest degree.

Here we have 2 with highest power 2 and other prime factors 3 and 5. Multiply all these to get LCM.

LCM of 20 and 12 = 2×2×3×5=22×3×5=60

HCF By Prime Factorization Method:-

Given natural numbers are written as the product of prime factors. To obtain the highest common factor multiply all the common prime factors with the lowest degree (power).

Example 1:

Find the HCF of 20 and 12 by prime factorization method.

Solution:

Step 1: To find HCF of 20 and 12 write each number as a product of prime factors.

20 = 2 × 2 × 5 = 22 × 5

12 = 2 × 2 × 3 = 22 × 3

Step 2: Multiply all the common prime factors with the lowest degree.

Here we have only 2 as a common prime factor with the lowest power of 2.

HCF of 20 and 12 = 4