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Least Common Multiple of an arbitrary number of positive integers

  1. Jan 23, 2014 #1
    I need an algorithm for LCM(k1, k2, ..., kn).

    Here's what I was thinking:

    • any number ki that divides evenly into another number kj, set ki = 1
    • return k1*k2*...*kn

    I'm having trouble implementing it, though.

    Code (Text):

    int LCM(int* numsPtr, int size) {
        // assume size > 1 and that array only contains non-negative numbers
        std::vector<int> numsVec(numsPtr, numsPtr + size);
        std::sort(numsVec.begin(), numsVec.begin() + size);
        for (int k = 0; k < size - 1; ++k) {
            for (int j = k; j < size; ++j) {
                if (numsVec[j] % numsVec[k] == 0) {
                    numsVec[k] = 1;
        int product = 1;
        for (int k = 0; k < size; ++k)
                product *= numsVec[k];
        return product;
    Last edited: Jan 23, 2014
  2. jcsd
  3. Jan 25, 2014 #2
    What if you had k1=2*3, k2=2*5, k3=2*7? None evenly divides the other, but the LCM isn't k1*k2*k3, is it?
  4. Jan 25, 2014 #3


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    Science Advisor
    Homework Helper

    The naive way is to factorize all the numbers.

    A less naive way is to find their greatest common divisors. Some guy called Euclid found a neat way to do that.
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