# C Program to find LCM of two numbers

LCM (Least Common Multiple) of two numbers is the smallest number which can be divided by both numbers.
For example LCM of 15 and 20 is 60 and LCM of 5 and 7 is 35.

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

A simple solution is to find all prime factors of both numbers, then find union of all factors present in both numbers. Finally return product of elements in union.

An efficient solution is based on below formula for LCM of two numbers ‘a’ and ‘b’.

```   a x b = LCM(a, b) * GCD (a, b)

LCM(a, b) = (a x b) / GCD(a, b) ```

We have discussed function to find GCD of two numbers. Using GCD, we can find LCM.

Following is implementation of above idea.

## C

```// C program to find LCM of two numbers
#include <stdio.h>

// Recursive function to return gcd of a and b
int gcd(int a, int b)
{
// base case
if (a == b)
return a;

// a is greater
if (a > b)
return gcd(a-b, b);
return gcd(a, b-a);
}

// Function to return LCM of two numbers
int lcm(int a, int b)
{
return (a*b)/gcd(a, b);
}

// Driver program to test above function
int main()
{
int a = 15, b = 20;
printf("LCM of %d and %d is %d ", a, b, lcm(a, b));
return 0;
}
```

## Java

```// Java program to find LCM of two numbers.
class Test
{
// Recursive method to return gcd of a and b
static int gcd(int a, int b)
{
// Everything divides 0
if (a == 0 || b == 0)
return 0;

// base case
if (a == b)
return a;

// a is greater
if (a > b)
return gcd(a-b, b);
return gcd(a, b-a);
}

// method to return LCM of two numbers
static int lcm(int a, int b)
{
return (a*b)/gcd(a, b);
}

// Driver method
public static void main(String[] args)
{
int a = 15, b = 20;
System.out.println("LCM of " + a +" and " + b + " is " + lcm(a, b));
}
}
```

Output:

`LCM of 15 and 20 is 60`

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