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It has to do with factorials, the lowest 3 consecutive integers are 1, 2, and 3 multiply them together and you get 6, this happens with any number of consecutive integers when you multiply the lowest ones together, the answer is a factor of any of the same number of consecutive integers, i.e. 1x2x3x4x5=120, the same as 56x57x58x59x60=655,381,440 divide that by 120 and you get 5,461,512

Every second number is a multiple of two: 2, 4, 6, 8, etc. Every third number is a multiple of three: 3, 6, 9, 12, etc. So when you take a group of three consecutive integers, you are sure to get at least one multiple of two and one multiple of 3. When you multiply a multiple of two by a multiple of three, you get a multiple of 6.

Q: If you take the 3 numbers in any consecutive integers and multiply them together to get a new number that new number will always be a multiple of 6 why is this?

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