What is the smallest positive integer that is divisible by both 12 and 16?

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  1. 48
  2. 60
  3. 96
  4. 16 

Answer (Detailed Solution Below)

Option 1 : 48
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Detailed Solution

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Given:

What is the smallest positive integer that is divisible by both 12 and 16?

Formula used:

To find the smallest positive integer divisible by both numbers, we use the Least Common Multiple (LCM).

Calculation:

Prime factorization of 12: 12 = 22 × 3

Prime factorization of 16: 16 = 24

LCM = Highest power of all prime factors

⇒ LCM = 24 × 3

⇒ LCM = 16 × 3

⇒ LCM = 48

∴ The correct answer is 48.

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