My nine year old asked this question at lunch today: Is there a number that is divisible by everything that is half or less than the number?
I immediately answered, "No. I mean, 6. But not for any number bigger than 6."
So I tried to think why that was true, and my first efforts didn't quite work. I did come up with a proof, but it isn't as elegant as I hoped.
How would you prove this?