SOLUTION: "Show that the product of three consecutive natural numbers is divisible by 6"

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Question 451601: "Show that the product of three consecutive natural numbers is divisible by 6"
Answer by richard1234(7193) About Me  (Show Source):
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For any three consecutive natural numbers, at least one of them will be divisible by 2, and exactly one will be divisible by 3 (using modular arithmetic, the integers are 0,1,2; 1,2,0; or 2,0,1 mod 3). This implies that the product must be divisible by 6.