Skip to content
Related Articles

Related Articles

Improve Article
Find LCM of rational numbers
  • Difficulty Level : Hard
  • Last Updated : 21 Jun, 2021

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

 

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

Javascript




<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>

Output: 
 



30/1

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer DSA Live Classes




My Personal Notes arrow_drop_up
Recommended Articles
Page :