# Find the LCM and HCF of the following integers by applying the prime factorization method:12, 15 and 21

Given: 12, 15 and 21.

To find: Here we have to find the LCM and HCF of the given integers by applying the prime factorization method.

Solution:

Calculating LCM and HCF using prime factorization method:

Writing the numbers as a product of their prime factors:

Prime factorisation of 12:

• $2\ \times\ 2\ \times\ 3\ =\ 2^2\ \times\ 3^1$

Prime factorisation of 15:

• $3\ \times\ 5\ =\ 3^1\ \times\ 5^1$

Prime factorisation of 21:

• $3\ \times\ 7\ =\ 3^1\ \times\ 7^1$

Multiplying the highest power of each prime number these values together:

$2^2\ \times\ 3^1\ \times\ 5^1\ \times\ 7^1\ =\ 420$

LCM(12, 15, 21)  $=$  420

Multiplying all common prime factors:

$3^1\ =\ 3$

HCF(12, 15, 21)  $=$  3

So, the LCM and HCF of 12, 15 and 21 are 420 and 3 respectively.

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Updated on: 10-Oct-2022

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