# 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

`// 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; ` `} ` |

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Output:

30/1

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