Prove that the product of 3 consecutive integers is divisible by 6

If you set the three consecutive integers to be n, n+1 and n+2, we know that one of the numbers must be divisible by 2 and one must be divisible by 3. For example if you had your three numbers as: 5, 6, 7, one is divisible by 3 and one is divisible by 2, as this is the case with all consecutive three numbers. Therefore as we are multiplying the numbers together, multiplying a multiple of 3 and a multiple of 2 gives us a multiple of 6. Hence the product will be divisible by 6.