How to Find the Smallest Integer with Specific Remainders?

[CalculusSandwich]

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?

 

[I like Serena]

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.

 

[Norwegian]

If you for some reason do not like the number 4, you have to add the lcm of your moduli to get the next.