**Solution:**

True.

**Justification:**

At least one out of every three consecutive positive integers is divisible by 2.

Therefore, The product of three consecutive positive integers is divisible by 2.

At least one out of every three consecutive positive integers is divisible by 3.

Therefore, The product of three consecutive positive integers is divisible by 3.

Since the product of three consecutive positive integers is divisible by 2 and 3.

Hence, It is divisible by 6 also.