find-lcm()

Step 1: Understanding the Problem

The task at hand is to find the least common multiple (LCM) of two given integers. The LCM of two numbers can be found by determining the multiples of each number and then finding the least number which is common to both sets of multiples. In programming terms, you can solve this by using a while loop until you find the LCM.

In Java, you would start off your function like this:

public static int findLCM(int num1, int num2) {
    int lcm = Math.max(num1, num2);
    ...
}

Step 2: Implementing the Loop

Next, you will add a while loop inside the function. The loop should continue as long as the LCM is not a multiple of both numbers. This can be checked using the modulo operator (%).

public static int findLCM(int num1, int num2) {
    int lcm = Math.max(num1, num2);
    while (true) {
        if (lcm % num1 == 0 && lcm % num2 == 0) {
            break;
        }
        lcm++;
    }
    ...
}

Step 3: Returning the Result

Once the loop ends, it means that the LCM has been found, so you can return that number from the function.

public static int findLCM(int num1, int num2) {
    int lcm = Math.max(num1, num2);
    while (true) {
        if (lcm % num1 == 0 && lcm % num2 == 0) {
            break;
        }
        lcm++;
    }
    return lcm;
}

Step 4: Testing the Function

After implementing the function, you should always test it to make sure it works as expected. You can do this by calling the function with test cases for which you know the expected output.

public static void main(String[] args) {
    System.out.println(findLCM(4, 5));  // Output: 20
    System.out.println(findLCM(7, 3));  // Output: 21
}

Conclusion

In conclusion, to find the LCM of two numbers in Java, you start by initializing the LCM as the larger of the two numbers. Then, you keep incrementing the LCM until it becomes a multiple of both numbers. Once it does, you have found the LCM, so you can return it from the function.