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

Given: 8, 9 and 25.

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 8:

• $2\ \times\ 2\ \times\ 2\ =\ 2^3$

Prime factorisation of 9:

• $3\ \times\ 3\ =\ 3^2$

Prime factorisation of 25:

• $5\ \times\ 5\ =\ 5^2$

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

$2^3\ \times\ 3^2\ \times\ 5^2\ =\ 1800$

LCM(8, 9, 25)  $=$  1800

Multiplying all common prime factors: 

There is no common prime factor. So,

HCF(8, 9, 25)  $=$  1

So, the LCM and HCF of 8, 9 and 25 are 1800 and 1 respectively.

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Updated on: 10-Oct-2022

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