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Grace is thinking of a positive number, less than 500, that is divisible by every number from 1 to 10 (inclusive), with one exception. What number is she thinking of? Prove that the answer is unique.

 

I figured out that the number is 360 because it's the least common multiple of 1, 2, 3, 4, 5, 6, 8, 9, and 10, but I'm not sure how to prove that the answer is unique. I would really appreciate some help with this!!!

 Jul 14, 2020
 #1
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Perhaps this link might help: 

 

https://web2.0calc.com/questions/i-am-thinking-of-a-positive-number-less-than-500-that-is-divisible-by-every-number-from-1-to-10-inclusive-with-one-exception-what-numb

 Jul 14, 2020
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Thank you for the link!! I solved it the same way as Melody, but I am also struggling to find a way to prove it, so if possible I would like some help with that. 

mathmathj28  Jul 14, 2020

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