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!!!
Perhaps this link might help: