What is the LCM of 84,120,138?

Given: 84,120,138.

To find: We have to find the LCM of 84,120,138.

Solution: 

Using Prime factorisation method to calculate the LCM:

Prime factorisation of 84:

• 2 x 2 x 3 x 7 = 2² x 3¹ x 7¹

Prime factorisation of 120:

• 2 x 2 x 2 x 3 x 5 = 2³ x 3¹ x 5¹

Prime factorisation of 138:

• 2 x 3 x 23 = 2¹ x 3¹ x 23¹

Highest power of each prime number:

• 2³ , 3¹ , 7¹ , 5¹ , 23¹

Multiply these values together:

• 2³ x 3¹ x 7¹ x 5¹ x 23¹ = 19320

Thus,

LCM(84,120,138) = 19320

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Updated on: 10-Oct-2022

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