**Exercise**:

Write a Java Program to find the Lowest Common Multiple (LCM) of two numbers.

#### 1.Calculate using While loop

**Click Here to View the Solution!**

```
public class LCMFinder {
public static void main(String[] args) {
int num1 = 60, num2 = 240, lcm;
// maximum number between n1 and n2 is stored in lcm
lcm = (num1 > num2) ? num1 : num2;
// Always true
while(true) {
if( lcm % num1 == 0 && lcm % num2 == 0 ) {
System.out.printf("The LCM of %d and %d is %d.", num1, num2, lcm);
break;
}
++lcm;
}
}
}
```

**Click Here to View the Output!**

The LCM of 60 and 240 is 240.

**Click Here to View the Explanation!**

- This program is used for finding the Lowest Common Multiple (LCM) of two numbers by using the while loop.
- Initially, two integer numbers
`num1`

and`num2`

are initialized as`num1`

= 60 and`num2 = 240`

of which the`lcm`

needs to be found. - Since, the value of LCM must be greater or equal to the largest number, the initial value of the variable
`lcm`

is set to be the largest of the two numbers`num1`

and`num2`

. - For the
`lcm`

of two numbers, it should have zero remainder with both numbers. Therefore, in the infinite while loop, the value of`lcm`

is checked to find out whether it is exactly divisible by the two numbers. - If the
`lcm`

is found, the program can break out of the loop and print the output else, the value of`lcm`

is incremented, and the`while loop`

is run again. This is done until the`lcm`

is found. - In the end, the LCM is displayed on the screen.

#### 2. CALCULATE USING GCD

**Click Here to View the Solution!**

```
public class LCMFinder {
public static void main(String[] args) {
int num1 = 60, num2 = 240, gcd = 1;
for(int i = 1; i <= num1 && i <= num2; ++i)
{
// Condition to check if i is factor of both numbers
if(num1 % i == 0 && num2 % i == 0)
gcd = i;
}
int lcm = (num1 * num2) / gcd;
System.out.printf("The LCM of %d and %d is %d.", num1, num2, lcm);
}
}
```

**Click Here to View the Output!**

The LCM of 60 and 240 is 240.

**Click Here to View the Explanation!**

- This program is used for finding the LCM of two numbers by using their GCD. It uses the while and for loop.
- Initially, two numbers,
`num1`

and`num2`

are initialized as`num1 = 60`

and`num2 = 240`

of which the gcd and lcm is to be found. And another variable gcd is initialized as`gcd = 1`

. - The gcd of the two numbers is calculated through a condition set in the
`for loop.`

- After the gcd is found, the lcm of the two numbers is found using the following formula:
`(num1 * num2) / gcd`

. - As a result, the LCM of the given two numbers are displayed on the screen.