## Question regarding mod classes

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?
 PhysOrg.com science news on PhysOrg.com >> Galaxies fed by funnels of fuel>> The better to see you with: Scientists build record-setting metamaterial flat lens>> Google eyes emerging markets networks
 Recognitions: Homework Help 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.
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