Encuentra MCM de números racionales

Dada una array de números racionales, la tarea es encontrar el MCM de estos números.

Ejemplos: 

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

Primero encuentre el mcm de todos los numeradores de los números racionales, luego encuentre el mcd de todos los denominadores de los números racionales y luego divida mcm de todos los numeradores/mcd de todos los denominadores, este es el mcm de los números racionales.
Fórmula:- 

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

Implementación:

// 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;
}

// JAVA program to find LCM of given array
import java.util.*;
 
class GFG
{
     
static class pair
{
    int first, second;
    public pair(int first, int second)
    {
        this.first = first;
        this.second = second;
    }
}
 
// get lcm of two numbers
static int LCM(int a, int b)
{
    return (a * b) / (__gcd(a, b));
}
static int __gcd(int a, int b)
{
    return b == 0? a:__gcd(b, a % b);    
}
 
// Finds LCM of numerators
static int lcmOfNumerator(Vector<pair> vect)
{
    // calculate the lcm of all numerators
    int lcm = vect.get(0).first;
    for (int i = 1; i < vect.size(); i++)
        lcm = LCM(vect.get(i).first, lcm);
 
    // return all numerator lcm
    return lcm;
}
 
// Get GCD of all the denominators
static int gcdOfDemoninators(Vector<pair> vect)
{
    // calculate the gcd of all the denominators
    int gcd = vect.get(0).second;
    for (int i = 1; i < vect.size(); i++)
        gcd = __gcd(vect.get(i).second, gcd);
 
    // return all denominator gcd
    return gcd;
}
 
// find lcm of all the rational number
static void lcmOfRationals(Vector<pair> vect)
{
    // return the LCM of all numerator/ GCD of all
    // denominator
    System.out.print(lcmOfNumerator(vect)+ "/"
        + gcdOfDemoninators(vect));
}
 
// Driver code
public static void main(String[] args)
{
    Vector<pair> vect = new Vector<pair>();
 
    // give rational number 2/7, 3/14, 5/3
    // make pair as a numerator and denominator
    vect.add(new pair(2, 7));
    vect.add(new pair(3, 14));
    vect.add(new pair(5, 3));
    lcmOfRationals(vect);
}
}
 
// This code is contributed by Rajput-Ji

# Python program to find LCM of given array
import math
 
# get lcm of two numbers
def LCM(a, b):
     
    return (a * b) // (math.gcd(a, b))
 
# Finds LCM of numerators
def lcmOfNumerator(vect):
 
    # calculate the lcm of all numerators
    lcm = vect[0][0]
    for i in range(1, len(vect)):
        lcm = LCM(vect[i][0], lcm)
     
    # return all numerator lcm
    return lcm
 
# Get GCD of all the denominators
def gcdOfDemoninators(vect):
     
    # calculate the gcd of all the denominators
    gcd = vect[0][1]
    for i in range(1, len(vect)):
        gcd = math.gcd(vect[i][1], gcd)
         
    # return all denominator gcd
    return gcd
 
# find lcm of all the rational number
def lcmOfRationals(vect):
     
    # return the LCM of all numerator/ GCD of all
    # denominator
    print(lcmOfNumerator(vect), "/",
            gcdOfDemoninators(vect), sep = "")
 
 
# Driver code
 
vect = []
 
# give rational number 2/7, 3/14, 5/3
# make pair as a numerator and denominator
vect.append((2, 7))
vect.append((3, 14))
vect.append((5, 3))
lcmOfRationals(vect)
 
# This code is contributed by SHUBHAMSINGH10

// C# program to find LCM of given array
using System;
using System.Collections.Generic;
 
class GFG
{
     
class pair
{
    public int first, second;
    public pair(int first, int second)
    {
        this.first = first;
        this.second = second;
    }
}
 
// get lcm of two numbers
static int LCM(int a, int b)
{
    return (a * b) / (__gcd(a, b));
}
static int __gcd(int a, int b)
{
    return b == 0? a:__gcd(b, a % b);    
}
 
// Finds LCM of numerators
static int lcmOfNumerator(List<pair> vect)
{
    // calculate the lcm of all numerators
    int lcm = vect[0].first;
    for (int i = 1; i < vect.Count; i++)
        lcm = LCM(vect[i].first, lcm);
 
    // return all numerator lcm
    return lcm;
}
 
// Get GCD of all the denominators
static int gcdOfDemoninators(List<pair> vect)
{
    // calculate the gcd of all the denominators
    int gcd = vect[0].second;
    for (int i = 1; i < vect.Count; i++)
        gcd = __gcd(vect[i].second, gcd);
 
    // return all denominator gcd
    return gcd;
}
 
// find lcm of all the rational number
static void lcmOfRationals(List<pair> vect)
{
    // return the LCM of all numerator/ GCD of all
    // denominator
    Console.Write(lcmOfNumerator(vect)+ "/"
        + gcdOfDemoninators(vect));
}
 
// Driver code
public static void Main(String[] args)
{
    List<pair> vect = new List<pair>();
 
    // give rational number 2/7, 3/14, 5/3
    // make pair as a numerator and denominator
    vect.Add(new pair(2, 7));
    vect.Add(new pair(3, 14));
    vect.Add(new pair(5, 3));
    lcmOfRationals(vect);
}
}
 
// This code is contributed by 29AjayKumar

<script>
// JAVASCRIPT program to find LCM of given array
class pair
{
    constructor(first, second)
    {
        this.first = first;
        this.second = second;
    }
}
 
// get lcm of two numbers
function LCM(a, b) {
    return Math.floor((a * b) / (__gcd(a, b)));
}
 
function __gcd(a, b) {
    return b == 0 ? a : __gcd(b, a % b);
}
 
// Finds LCM of numerators
function lcmOfNumerator(vect)
{
 
    // calculate the lcm of all numerators
    let lcm = vect[0].first;
    for (let i = 1; i < vect.length; i++)
        lcm = LCM(vect[i].first, lcm);
 
    // return all numerator lcm
    return lcm;
}
 
// Get GCD of all the denominators
function gcdOfDemoninators(vect)
{
 
    // calculate the gcd of all the denominators
    let gcd = vect[0].second;
    for (let i = 1; i < vect.length; i++)
        gcd = __gcd(vect[i].second, gcd);
 
    // return all denominator gcd
    return gcd;
}
 
// find lcm of all the rational number
function lcmOfRationals(vect) {
    // return the LCM of all numerator/ GCD of all
    // denominator
    document.write(lcmOfNumerator(vect) + "/"
        + gcdOfDemoninators(vect));
}
 
// Driver code
 
let vect = [];
 
// give rational number 2/7, 3/14, 5/3
// make pair as a numerator and denominator
vect.push(new pair(2, 7));
vect.push(new pair(3, 14));
vect.push(new pair(5, 3));
lcmOfRationals(vect);
 
// This code is contributed by _SAURABH_JAISWAL
</script>

30/1

Complejidad de tiempo: O(n log(min(v))), donde v es el elemento mínimo del vector 
Espacio auxiliar: O(1)

Sugiera si alguien tiene una mejor solución que sea más eficiente en términos de espacio y tiempo.
Este artículo es una contribución de Aarti_Rathi . Escriba comentarios si encuentra algo incorrecto o si desea compartir más información sobre el tema tratado anteriormente.