Please try to find an answer for this ?????
When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

LCM of 2,3,4,5,6,7,8,9,10 = 
2 = 2 
3 = 3 
4 = 2^2 
5 = 5 
6 = 2 x 3 
7 = 7 
8 = 2^3 
9 = 3^2 
10 = 2 x5 

LCM = 2^3 x 3^2 x 5 x 7 
LCM = 8 x 6 x 5 x 7 = 2520. 

The answer you want is 
2520 - 1 = 2519. 

Checking 
2519/2 = 1259+ 1/2 
2519/3 = 839 + 2/3 
2519/4 = 629 + 3/4 
2519/5 = 503 + 4/5 
2519/6 = 419 + 5/6 
2519/7 = 359 + 6/7 
2519/8 = 314 + 7/8 
2519/9 = 279 + 8/9 
2519/10 = 215 + 9/10 

So the answer is 
2519 
  Since the LCM of those numbers is 2520 
All of them can divided 2520 without giving any remainders. 
So 2520-1; 
gives the remainder of 9 when divided by 10 
remainder 8 when divided by 9 
remainder 7 when divided by 8  and so on ......