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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

C++

// 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

// 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

# 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#

// 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 

Output:

30/1

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python

C#

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