Find LCM of rational number in C++

Here we will see how to find the LCM of Rational numbers. We have a list of rational numbers. Suppose the list is like {2/7, 3/14, 5/3}, then the LCM will be 30/1.

To solve this problem, we have to calculate LCM of all numerators, then gcd of all denominators, then the LCM of rational numbers, will be like −

$$LCM =\frac{LCM\:of\:all\:𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟𝑠}{GCD\:of\:all\:𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟𝑠}$$

Example

 Live Demo

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
int LCM(int a, int b) {
   return (a * b) / (__gcd(a, b));
}
int numeratorLCM(vector<pair<int, int> > vect) {
   int result = vect[0].first;
   for (int i = 1; i < vect.size(); i++)
      result = LCM(vect[i].first, result);
   return result;
}
int denominatorGCD(vector<pair<int, int> >vect) {
   int res = vect[0].second;
   for (int i = 1; i < vect.size(); i++)
      res = __gcd(vect[i].second, res);
   return res;
}
void rationalLCM(vector<pair<int, int> > vect) {
   cout << numeratorLCM(vect) << "/"<< denominatorGCD(vect);
}
int main() {
   vector<pair<int, int> > vect;
   vect.push_back(make_pair(2, 7));
   vect.push_back(make_pair(3, 14));
   vect.push_back(make_pair(5, 3));
   cout << "LCM of rational numbers: "; rationalLCM(vect);
}

Output

LCM of rational numbers: 30/1

Arnab Chakraborty

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Updated on: 21-Oct-2019

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