Find LCM of 24, 36, 108, 192

Given: 

Given numbers are 24, 36, 108 and 192.

To do: 

We have to find the LCM of the given integers.

Solution:

Writing the numbers as a product of their prime factors:

Prime factorisation of 24:

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

Prime factorisation of 36:

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

Prime factorisation of 108:

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

Prime factorisation of 192:

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

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

$2^6\ \times\ 3^3\ =64\times27$

LCM(24, 36, 108, 192) $=1728$  

Therefore, LCM of 24, 36, 108, 192 is 1728.

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Updated on: 10-Oct-2022

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