# 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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