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Let P be the product of three consecutive integers.  What is the greatest integer that always divides P?

 Jun 14, 2020
 #1
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I personally don't think that this question makes much sense. If you think about it - there are infinite consecutive integers, therefore, there are infinite integers that divide by P. Are there any numbers in this question that I am not aware of? If so, please add them (it'll help a lot). Thanks!

 Jun 14, 2020
 #2
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I believe the answer is 6. After testing out a few cases, it becomes obvious that there is always a multiple of 2 and a multiple of 3 in three consecutive integers. 

I'm don't know a rigorous way to prove it though.

 Jun 14, 2020
 #3
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Any three consecutive numbers you choose, one of them is ALWAYS a multiple of 2  and  one is ALWAYS a multiple of 3. Therefore: 2 x 3 = 6 will ALWAYS divide the product of 3 consecutive numbers.

 Jun 14, 2020

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