Prove that the product of three consecutive positive integers is divisible by `6`.

Explanation

To prove that the product of three consecutive positive integers is divisible by 6, we will follow a structured approach using mathematical induction.

### Step 1: Define the three consecutive integers
Let the three consecutive positive integers be represented as:
- \( n - 1 \)
- \( n \)
- \( n + 1 \)

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