Find the LCM and HCF of the following integers by applying the prime factorization method:
84, 90 and 120

Given: 84, 90 and 120.

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 84:

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

Prime factorisation of 90:

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

Prime factorisation of 120:

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

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

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

LCM(84, 90, 120)  $=$  2520

Multiplying all common prime factors: 

$2^1\ \times\ 3^1\ =\ 6$

HCF(84, 90, 120)  $=$  6

So, the LCM and HCF of 84, 90 and 120 are 2520 and 6 respectively.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

2K+ Views

Kickstart Your Career

Get certified by completing the course

Get Started