smc

Question

A number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, by 8 leaves a remainder of 7, etc., down to where, when divided by 2, it leaves a remainder of 1, is:

Accepted Answer

If we add 1 to the number, it becomes divisible by 10, 9, 8, , 2, 1. The LCM of 1 through 10 is 2520, therefore the number we want to find is 2520-1=2519