Find LCM of rational numbers

Given an array of rational numbers, the task is to find the LCM of these numbers.

Examples:

Input : vect[] = {2/7, 3/14, 5/3}
Output : 30/1

Input : vect[] = {3/14, 5/3}
Output : 15/1

Input : vect[] = {3/4, 3/2}
Output : 3/2



First find the lcm of all numerator of rational number then find the gcd of all the denominator of rational number then divide lcm of all numerator/ gcd of all the denominator this the lcm of rational number’s.

Formula:-

      LCM of all the numerator of Rational number's
lcm = -----------------------------------------------
      GCD of all the denominator of Rational number's
filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP program to find LCM of given array
#include <bits/stdc++.h>
using namespace std;
  
// get lcm of two numbers
int LCM(int a, int b)
{
    return (a * b) / (__gcd(a, b));
}
  
// Finds LCM of numerators
int lcmOfNumerator(vector<pair<int, int> > vect)
{
    // calculate the lcm of all numerators
    int lcm = vect[0].first;
    for (int i = 1; i < vect.size(); i++) 
        lcm = LCM(vect[i].first, lcm); 
  
    // return all numerator lcm
    return lcm;
}
  
// Get GCD of all the denominators
int gcdOfDemoninators(vector<pair<int, int> > vect)
{
    // calculate the gcd of all the denominators
    int gcd = vect[0].second;
    for (int i = 1; i < vect.size(); i++) 
        gcd = __gcd(vect[i].second, gcd); 
  
    // return all denominator gcd
    return gcd;
}
  
// find lcm of all the rational number
void lcmOfRationals(vector<pair<int, int> > vect)
{
    // return the LCM of all numerator/ GCD of all 
    // denominator
    cout << lcmOfNumerator(vect) << "/"
        << gcdOfDemoninators(vect);
}
  
// Driver code
int main()
{
    vector<pair<int, int> > vect;
  
    // give rational number 2/7, 3/14, 5/3
    // make pair as a numerator and denominator
    vect.push_back(make_pair(2, 7));
    vect.push_back(make_pair(3, 14));
    vect.push_back(make_pair(5, 3));
    lcmOfRationals(vect);
    return 0;
}

chevron_right


Output:

30/1


My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.