Find the LCM and HCF of the following integers by applying the prime factorization method:
40, 36 and 126

Given: 40, 36 and 126.

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 40:

• $2\ \times\ 2\ \times\ 2\ \times\ 5\ =\ 2^3\ \times\ 5^1$

Prime factorisation of 36:

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

Prime factorisation of 126:

• $2\ \times\ 3\ \times\ 3\ \times\ 7\ =\ 2^1\ \times\ 3^2\ \times\ 7^1$

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

$2^3\ \times\ 3^2\ \times\ 5^1\ \times\ 7^1\ =\ 2520$

LCM(40, 36, 126)  $=$  2520

Multiplying all common prime factors: 

$2^1\ =\ 2$

HCF(40, 36, 126)  $=$  2

So, the LCM and HCF of 40, 36 and 126 are 2520 and 2 respectively.

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Updated on: 10-Oct-2022

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