Find the LCM of 48, 64, 72, 96, 106.

Given: 48, 64, 72, 96, 106.

To find: Here we have to find LCM of 48, 64, 72, 96, 106.

Solution:

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

Prime factorization of 48:

• 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3 = 2⁴ $\times$ 3¹

Prime factorization of 64:

• 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 = 2⁶

Prime factorization of 72:

• 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 = 2³ $\times$ 3²

Prime factorization of 96:

• 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3 = 2⁵ $\times$ 3¹

Prime factorization of 106:

• 2 $\times$ 53 = 2¹ $\times$ 53¹

Finding the highest power of each prime number:

• 2⁶ , 3² , 53¹

Multiplying these values together:

• 2⁶ $\times$ 3² $\times$ 53¹ = 30528

Thus,

LCM(48, 64, 72, 96, 106) = 30528

So, LCM of 48, 64, 72, 96, 106 is 30528.

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Updated on: 10-Oct-2022

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