Find the LCM Of 40, 144 and 180.

Given: 40, 144, and 180

To find: We have to find the LCM of 40, 144, and 180.

Solution: 

Writing all the numbers as a product of their prime factors:

Prime factorization of 40:

• 2 $\times $ 2 $\times $ 2 $\times $ 5 = 2³ $\times $ 5¹

Prime factorization of 144:

• 2 $\times $ 2 $\times $ 2 $\times $ 2 $\times $ 3 $\times $ 3 = 2⁴ $\times $ 3²

Prime factorization of 180:

• 2 $\times $ 2 $\times $ 3 $\times $ 3 $\times $ 5 = 2² $\times $ 3² $\times $ 5¹

Find highest power of each prime number:

2⁴ , 3² , 5¹

Multiply these values together:

2⁴ $\times $ 3² $\times $ 5¹ = 720

Thus,

LCM(40, 144, 180) = 720

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Updated on: 10-Oct-2022

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