Multiple Surprises Ethan

The first, and most obvious solution, is 1,2,3,4,5,6,7,8,9,10. 

Any number that is a multiple of 2520 more than this solution works, since 2520 is divisible by every number from 1 to 10. Anything else won't work, since it will be a non-multiple of one of the numbers more than a multiple, which cannot be a multiple.