findLCM()

Step 1: Understanding the Problem

We need to create a function in JavaScript that takes in two numbers and returns their Lowest Common Multiple (LCM). The LCM of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b. So our task is to write a function called findLCM which takes two numbers as inputs and returns their LCM.

function findLCM(a, b) {
  // Our code will go here
}

Step 2: Identifying a Mathematical Helper

Since we're solving a mathematical problem, it's best to use mathematical properties. In this case, we can use the fact that “a*b = gcd(a,b)*lcm(a,b)”. So we can say that lcm(a, b) = (a * b) / gcd(a, b) where gcd(a, b) is the greatest common divisor of a and b.

function findLCM(a, b) {
  // To implement this we first need to find the gcd
  let gcd = findGCD(a, b);

  // Then we find the LCM
  let lcm = (a * b) / gcd;
  return lcm;
}

Step 3: Implementing the GCD Helper Function

We'll write a helper function called findGCD that takes in 2 numbers and returns their greatest common divisor. For this, we can use the Euclidean algorithm. The Euclidean algorithm is a way to find the greatest common divisor of two positive integers a and b. It starts with the division of a by b and takes the remainder r. Then, replace a by b and replace b by r, and repeat the division.

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

Step 4: Integrating the GCD Helper Function

Now that we have our helper function to get the gcd, we can use it in our findLCM function.

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

function findLCM(a, b) {
  let gcd = findGCD(a, b);
  let lcm = (a * b) / gcd;
  return lcm;
}

Step 5: Testing our function

Let's run some tests on our function to make sure it's working as expected.

console.log(findLCM(12, 15)); // Expected output: 60
console.log(findLCM(5, 10)); // Expected output: 10
console.log(findLCM(7, 5)); // Expected output: 35

In conclusion, we have successfully implemented a JavaScript function to find the Lowest Common Multiple of two given numbers by using the mathematical connection with greatest common divisor. This function can be used as a utility in many numeric or algebraic JavaScript applications. The final, fully-implemented function is as follows:

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

function findLCM(a, b) {
  let gcd = findGCD(a, b);
  let lcm = (a * b) / gcd;
  return lcm;
}