How to find the original sum using remainders left by grouping them in 3, 5 and then 7?

Question

Han Sin, a Chinese General is able to count the number of soldiers he had. He grouped them in 3, then 5 and the 7 and took note of the remainder in each case. Using the remainders, he could calculate the exact number of soldiers. How did he do it?

Answer 1

the LCM of these nos is 105.
so 35+remainderof 3,21+remainder of 5 and 15+remainder of7 will give the no of soldiers

Answer 2

if the remainder is 1 in all three cases, the number of soldiers can be 1 or 106 or 211 or 316...
(1 + 3*5*7, 1 + 3*5*7*2, 1 + 3*5*7*3, ... )
There are unlimited possibilities. So a definite answer is not possible.