Find the smallest positive integer which when divided by 12, by 17, by 45 or by 70 gives a remainder of 4 in each case. I know I can approach this problem by writing the equivalence classes. x=4mod12 x=4mod17 x=4mod45 or x=4mod70 I also know I can find x by multiplying 12*17*45 + 4, but this isn't the smallest positive integer. Can someone help me with a formula I can use?
Erm... how about the solution x=4? It is a solution and I don't think there are any smaller positive integers that are also a solution.
If you for some reason do not like the number 4, you have to add the lcm of your moduli to get the next.