Question regarding mod classes

  1. 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?
     
  2. jcsd
  3. I like Serena

    I like Serena 6,192
    Homework Helper

    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.
     
  4. 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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