calculateLCMArray()

Step 1: Understand the Problem

The first thing we need to do is to understand what we are trying to solve. Given an array of numbers, our goal is to find the least common multiple (LCM) of all those numbers. The LCM of two integers a and b is the smallest positive integer that is divisible by both a and b. For instance, for 5 and 7, the LCM is 35.

To solve this problem, we will need to write a helper function to find the LCM of two numbers, and then use this helper function to find the LCM of the entire array.

Step 2: Write the Helper Function

For the helper function, we will calculate the LCM of two numbers. We will use the formula lcm(a, b) = |a*b|/gcd(a, b), where gcd(a, b) is the greatest common divisor of a and b.

Now, let's implement this helper function in JavaScript:

function lcm(a, b) {
    return Math.abs(a*b) / gcd(a, b);
}

Here we implicitly use a predefined gcd function. If it's not available we have to define it before:

function gcd(a, b) {
    if (b == 0) {
        return a;
    } else {
        return gcd(b, a % b);
    }
}

Here, the gcd function uses the Euclidean algorithm to find the greatest common divisor of two numbers.

Step 3: Use the Helper Function to Find the LCM of the Array

Next, we want to iterate over our array and calculate the LCM. To start, we will set our initial LCM to the first number in the array. Then, we will iterate over the rest of the array and update our LCM each time by finding the LCM of the current LCM and the next number in the array.

function calculateLCMArray(nums) {
    var currentLCM = nums[0];

    for (var i = 1; i < nums.length; i++) {
        currentLCM = lcm(currentLCM, nums[i]);
    }

    return currentLCM;
}

Step 4: Test the Function

Before we finalize our solution, we should test it with some inputs to make sure it works as expected.

console.log(calculateLCMArray([3, 5, 7]));  // 105
console.log(calculateLCMArray([1, 2, 3, 4, 5, 6]));  // 60

Step 5: Conclusion

Finally, putting it all together we get the full function to calculate the least common multiple of an array of numbers:

function gcd(a, b) {
    if (b == 0) {
        return a;
    } else {
        return gcd(b, a % b);
    }
}

function lcm(a, b) {
    return Math.abs(a*b) / gcd(a, b);
}

function calculateLCMArray(nums) {
    var currentLCM = nums[0];

    for (var i = 1; i < nums.length; i++) {
        currentLCM = lcm(currentLCM, nums[i]);
    }

    return currentLCM;
}

console.log(calculateLCMArray([3, 5, 7]));      // 105
console.log(calculateLCMArray([1, 2, 3, 4, 5, 6]));  // 60

By breaking the problem down and tackling each part separately, we successfully created a function that calculates the least common multiple for an array of numbers in JavaScript.