# Java Program to Find LCM of two Numbers

## What is LCM of Numbers ?

The smallest positive integer that is a multiple of two or more numbers is known as the LCM (Least Common Multiple). We can use prime factorization to find the LCM by taking the product of the highest powers of each prime factor, or we can list the multiples of each number and find the lowest one that appears in all the lists.

## Steps to Find the Largest Among Three Numbers :

1. Each integer should be divided into its prime elements.
2. List every distinct prime factor that appears in every number.
3. Choose the highest power that appears across all the numbers for each distinct prime factor.
4. Multiply all the prime factors together, using the highest power for each factor.

### Example to determine the LCM of 6 and 8 :

1. Divide 6 into its prime elements to find: 6 = 2 * 3
2. Factor 8 into its main components: 8 = 2 * 2 * 2
3. Find the distinct prime factors: 2 and 3.
4. Take into account the maximum power for 2 in either of the factorizations: 2^3 = 8.
5. Choose the highest power that occurs for 3, then: 3^1 = 3.
6. Add the prime elements together to get: LCM(6, 8) = 2^3 * 3^1 = 24.

So the LCM of 6 and 8 is 24.

### Pseudo Code using while loop :

```function LCM(a, b):
lcm = max(a, b)
while True:
if lcm % a == 0 and lcm % b == 0:
return lcm
lcm += max(a, b)
```

### Example 1 :

Run
```public class Main {
public static void main(String[] args) {
int a = 24, b = 36;
int lcm = findLCM(a, b);
System.out.println("LCM of " + a + " and " + b + " is " + lcm);
}

public static int findLCM(int a, int b) {
int lcm = Math.max(a, b);
while (true) {
if (lcm % a == 0 && lcm % b == 0) {
return lcm;
}
lcm += Math.max(a, b);
}
}
}

```

### Output :

```LCM of 24 and 36 is 72
```

### Example 2 :

Run
```public class Main {
public static void main(String[] args) {
int a = 24, b = 36;
int gcd = findGCD(a, b);
int lcm = (a * b) / gcd;
System.out.println("LCM of " + a + " and " + b + " is " + lcm);
}

public static int findGCD(int a, int b) {
if (b == 0) {
return a;
}
return findGCD(b, a % b);
}
}

```

### Output :

```LCM of 24 and 36 is 72
```

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