When the positive integer x is divided by each of 4, 5, 6, and 7, it has a remainder of 3. What is the sum of the three smallest possible values of x?
Using CRT + MMI
x mod 4 = 3 x mod 5 = 3 x mod 6 = 3 x mod 7 = 3, solve for x
LCM[4, 5, 6, 7]==420
x =420n + 3, where n =0, 1, 2, 3.......etc.
The smallest value of x is when n = 0, which means x = 3
So, the sum of 3 smallest values of x are:
3 + 423 + 843 ==1,269
