Dr. Bos' Problem:

A Problem of Remainders

A number, if divided by 10, leaves a remainder of 9; divided by 9 leaves a remainder of 8; divided by 8 leaves a remainder of 7; divided by 7 leaves a remainder of 6; divided by 6 leaves a remainder of 5; divided by 5 leaves a remainder of 4; divided by 4 leaves a remainder of 3; divided by 3 leaves a remainder of 2; divided by 2 leaves a remainder of 1? One answer is 14,622,042,959. Find a smaller solution. (Can you find the smallest such number?)