LCM of Two Numbers in C++

In this post, we will develop a program to find LCM of two numbers in C++ programming language.  

Least or lowest common multiple (LCM) of two integers a and b is the smallest positive number that is divisible by both a and b. Example:- LCM of 12 and 15 is 60 because 60 is divisible by both 12 and 15.

// C++ program to find LCM
#include<iostream>
using namespace std;
int main()
{
  // declare variables
  int num1, num2, max;

  // take input
  cout << "Enter two Integers: ";
  cin >> num1 >> num2;

  // maximum value between num1 and num2
  max = (num1 > num2) ? num1 : num2;

  while(true)
  {
    if(max % num1 == 0 && max % num2 ==0)
    {
      cout << "LCM = " << max << endl;
      break;
    }
    else
      max++;
  }

  return 0;
}

Output for the different test-cases:-

Enter two Integers: 12 14
LCM = 84

Enter two Integers: 12 16
LCM = 48

Another program

// C++ program to find LCM
#include<iostream>
using namespace std;
int main()
{
  // declare variables
  int n1, n2, minMultiple;

  // take input
  cout << "Enter two Integers: ";
  cin >> n1 >> n2;

  // find smallest and largest number
  int smallest = (n1 < n2) ? n1 : n2;
  int largest = (n1 > n2) ? n1 : n2;

  // assign smallest number to minMultiple
  minMultiple = smallest;

  // loop
  while(true) 
  {
      if(minMultiple % largest == 0) 
     {
        // display result
        cout << "LCM = " << minMultiple <<endl;
        break;
      }

      minMultiple = minMultiple + smallest ;
  }

  return 0;
}

LCM of Two Numbers in C++ Using HCF

We can also find the LCM of two numbers in C++using HCF or GCD. For this we have to use the following Formula, The product of two numbers a and b is equal to the product of HCF(a,b) and LCM(a,b).

a*b = HCF(a,b) * LCM(a,b)

In the below program to find LCM of two numbers in C++; First, we find the HCF then using the above formula LCM will be calculated. The Formula used for this purpose is,

LCM(a,b) = (a*b) / HCF(a,b)

// C++ program to find LCM using HCF
#include<iostream>
using namespace std;
int main()
{
  // declare variable
  int num1, num2, hcf, temp, lcm;

  // take input
  cout << "Enter two Integers: ";
  cin >> num1 >> num2;

  // assign values
  hcf = num1;
  temp = num2;

  // calculate HCF
  while (hcf != temp)
  {
    ( hcf > temp ) ? (hcf -= temp) : (temp -= hcf);
  }

  // calculate LCM
  lcm = (num1 * num2) / hcf;

  // display result
  cout << "LCM = " << lcm << endl;

  return 0;
}

LCM of Two Numbers in C++ Using Recursion

We can also use the recursion technique to find the lcm of two numbers. A technique of defining the method/function that contains a call to itself is called the recursion. 

The recursive function/method allows us to divide the complex problem into identical single simple cases that can be handled easily. This is also a well-known computer programming technique: divide and conquer.

// C++ program to find LCM using HCF
#include< iostream>
using namespace std;

// global variable
static int common;

// function declaration
long lcm(int, int);

// main function
int main()
{
  // declare variable
  int num1, num2;

  // take input
  cout << "Enter two Integers: ";
  cin >> num1 >> num2;

  // display result
  cout << "LCM = " << lcm(num1, num2) << endl;

  return 0;
}

// function to find LCM value
long lcm(int n1, int n2)
{
  // increase common
  common += n2;
  if(common % n1 == 0)
     return common; // base case
  else
     return lcm(n1, n2); //general case
}

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