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

Implementation:

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# 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

Time Complexity: O(n log(min(v))), where v is the minimum element of vector
Auxiliary Space: O(1)

Please suggest if someone has a better solution which is more efficient in terms of space and time.

Find LCM of rational numbers

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