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 number am I thinking of? Prove that the answer is unique.

An explanation would be great!

It will be even

1*2*3*4*5 = 120 would be divisible by every integer from 1 - 10 inclusive except for 7 and 9

Multiplying this by 3 gives

1*2*3*3*4*5 = 1* 2*4*5*9 = 360

This will be divisible by 1, 2, 3, 4, 5, 6, 8, 9, and 10......it will not be divisible by 7