calculate-lcm-array()

Step 1: Thinking about the problem

The first step is to understand the problem. Here we are supposed to find the least common multiple (LCM) of a set of numbers. We know that LCM of two numbers a and b is the smallest positive integer that is perfectly divisible by both a and b. We can generalize this to find LCM of an array of numbers. We will start by finding LCM of the first two numbers, then find the LCM of the result and the third number, and so on. For finding the LCM of two numbers we will use the mathematical relation a*b = gcd(a,b) * lcm(a,b)

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

Step 2: Creating the function skeleton

We start by creating the function skeleton and then filling in the details. We define a function calculate_lcm_array that takes an array of integers as a parameter. The function itself doesn't return anything yet.

public void calculate_lcm_array(int[] numbers) {
    // Logic here
}

Step 3: Implementing the logic for LCM calculation

Now we will fill in the logic inside our function. As mentioned before, we will calculate the LCM iteratively. We start by storing the first number in the array in a variable lcm. Then for each subsequent number in the array, we calculate the new LCM of this number and the current lcm. Finally, we return the lcm variable, which now holds the LCM of all numbers.

public int calculate_lcm_array(int[] numbers) {
    int lcm = numbers[0];
    for(int i=1; i<numbers.length; i++) { 
        lcm = (lcm * numbers[i]) / gcd(lcm, numbers[i]);
    }
    return lcm;
}

Step 4: Putting it all together

We finally put everything together, the function that calculates gcd and the function that calculates lcm. Here is the complete implementation:

public class Main {
    public static int gcd(int a, int b) {
        if (a == 0)
            return b; 
        return gcd(b % a, a); 
    }
    public static int calculate_lcm_array(int[] numbers) {
        int lcm = numbers[0];
        for(int i=1; i<numbers.length; i++) { 
            lcm = (lcm * numbers[i]) / gcd(lcm, numbers[i]);
        }
        return lcm;
    }
    public static void main(String[] args) {
        int[] numbers = {2, 7, 3};
        System.out.println(calculate_lcm_array(numbers));
    }
}

The main function is an example usage of the calculate_lcm_array function and it prints the LCM of the numbers in the numbers array.