LCM of two numbers in C++

The LCM stands for Least Common Multiple, which is used to get the smallest common multiple of two numbers (n1 and n2), and the common multiple should be divisible by the given numbers. A common multiple is a number that is common in both numbers. The representation of the LCM of two numbers, as LCM (a, b) or lcm (a, b).

For example, LCM of two positive numbers, as LCM (12, 24) is 24. Because both numbers 12 and 24 divides 24 without leaving any remainder. Similarly, the LCM of 3 and 4 is 12 because the smallest common multiple of both numbers is 12.

Algorithm of the LCM of two numbers

Step 1: Take two inputs from the user n1 and n2

Step 2: Store the smallest common multiple of n1 and n2 into the max variable.

Step 3: Validate whether the max variable is divisible by n1 and n2, print the max as the LCM of two numbers.

Step 4: Otherwise, the max value is updated by 1 on every iteration, and jump to step 3 to check the divisibility of the max variable.

Step 5: Terminate the program.

Program to get LCM of two numbers using if statement and while loop

Program1.cpp

#include <iostream>
using namespace std;
int main()
{
	int n1, n2, max_num, flag = 1;
	cout << " Enter two numbers: \n";
	cin >> n1 >> n2;	
	
	// use ternary operator to get the large number
	max_num = (n1 > n2) ? n1 : n2;
	
	while (flag)  
	{
		// if statement checks max_num is completely divisible by n1 and n2.
		if(max_num % n1 == 0 && max_num % n2 == 0)
		{
			cout << " The LCM of " <<n1 << " and " << n2 << " is " << max_num;
			break;
		}
		++max_num; // update by 1 on each iteration
	}
	return 0;
}

Output

Enter two numbers:
30
50
 The LCM of 30 and 50 is 150

Program to get the LCM of two numbers using while loop

Program2.cpp

#include <iostream>
using namespace std;

int main()
{
	// declare variables
	int num1, num2, lcm, gcd, temp;
	cout <<" Enter the first number: ";
	cin >> num1;
	cout <<" Enter the second number: ";
	cin >> num2;

	// assign num1 and num2 values to int a and b
	int a = num1;
	int b = num2;	
	// use while loop to define the condition
	while (num2 != 0)
	{
		temp = num2;
		num2 = num1 % num2;
		num1 = temp;
	}
	
	// assign num1 to gcd variable
	gcd = num1;
	lcm = (a * b) / gcd;
	cout << "\n LCM of " << a << " and " << b << " = " << lcm;
	return 0;
}

Output

Enter the first number: 15
 Enter the second number: 10

 LCM of 15 and 10 = 30

Program to get the LCM of two numbers using GCD

Program3.cpp

#include <iostream>
using namespace std;

// definition of getGCD() function
int getGCD( int n1, int n2)
{
// here if statement checks the given number is not equal to 0.
if ( n1 == 0 || n2 == 0)
return 0;

// if n1 equal to n2, return n1
if (n1 == n2)
return n1;

// if n1 is greater than n2, execute the followed statement
if ( n1 > n2)
return getGCD (n1 - n2, n2);

return getGCD (n1, n2 - n1);
}

// definition of getLCM() function
int getLCM (int n1, int n2)
{
/* divide the multiplication of n1 and n2 by getGCD() function to return LCM. */	
return (n1 * n2) / getGCD (n1,n2);
}

int main()
{
// declare local variables	
int n1, n2;
cout << " Enter two positive numbers: ";
cin >> n1 >> n2; // get numbers from user

// print the LCM(n1, n2)
cout << " \n LCM of " <<n1 << " and " << n2 << " is " << getLCM(n1, n2);
return 0;
} 

Output

Enter two positive numbers: 50
60

 LCM of 50 and 60 is 300

Program to get the LCM of two numbers using recursive function

Program 4.cpp

# include <iostream>
using namespace std;

// define the getGCD()  function and pass n1 and n2 parameter
int getGCD( int n1, int n2)
{
	if (n1 == 0)
	{
		return n2;		
	}

return getGCD(n2 % n1, n1);
}

// define the getLCM function to return the LCM
int getLCM( int n1, int n2)
{
	return (n1 / getGCD(n1, n2)) * n2;
}

int main()
{
	// declare local variable
	int num1, num2;
	cout << " Enter two numbers: " <<endl;
	cin >> num1 >> num2;
	cout << " LCM of two numbers " <<num1 <<" and " << num2 << " is " << getLCM(num1, num2);
}

Output

Enter two numbers:
12
36
 LCM of two numbers 12 and 36 is 36

Program to get the LCM of multiple array elements using function and while loop

Program5.cpp

#include <iostream>
using namespace std;
int lcm_num (int n1, int n2)
{
	int max;
	max = (n1 > n2) ? n1 : n2;
	while (true)
	{
		if (max % n1 == 0 && max % n2 ==0)
		return max;
		max++;
	}
}

// definition of lcm_array() function
int lcm_array (int arr[], int num)
{
	int i;
	int lcm = lcm_num( arr[0], arr[1]);
	
	// use for loop to get the lcm
	for (i = 2; i < num; i++)
	{
		lcm = lcm_num(lcm , arr[i]);
	}
	return lcm;
	
}

int main()
{	
	// declare integer array
	int arr[] = {10, 5, 15, 30};
	int num = sizeof(arr) / sizeof(arr[0]); // get the number of elements
	cout << " LCM of multiple array elements is: " << lcm_array(arr, num);
}

Output