Finding the least common multiple of a range of numbers in JavaScript?

We are required to write a JavaScript function that takes in an array of exactly two numbers specifying a range.

The function should then calculate the least common multiple of all the numbers within that range and return the final result.

Understanding LCM and GCD

To find the LCM of multiple numbers, we first need helper functions for GCD (Greatest Common Divisor) and LCM of two numbers:

• GCD: The largest number that divides both numbers evenly
• LCM: The smallest positive number that is divisible by both numbers
• Formula: LCM(a, b) = (a × b) / GCD(a, b)

Implementation

const range = [8, 3];

const gcd = (a, b) => {
    return !b ? a : gcd(b, a % b);
}

const lcm = (a, b) => {
    return a * (b / gcd(a, b));
};

const rangeLCM = (arr = []) => {
    if (arr[0] > arr[1]) arr = [arr[1], arr[0]];
    
    let result = arr[0];
    for (let x = arr[0]; x 

840


How It Works

Let's trace through the example with range [8, 3]:


First, swap to [3, 8] since 8 > 3
Start with result = 3
LCM(3, 3) = 3
LCM(3, 4) = 12
LCM(12, 5) = 60
LCM(60, 6) = 60
LCM(60, 7) = 420
LCM(420, 8) = 840


Step-by-Step Example

// Let's see the process step by step
const rangeWithSteps = (arr = []) => {
    if (arr[0] > arr[1]) arr = [arr[1], arr[0]];
    
    let result = arr[0];
    console.log(`Starting with: ${result}`);
    
    for (let x = arr[0]; x 

Starting with: 5
LCM(5, 5) = 5
LCM(5, 6) = 30
LCM(30, 7) = 210
LCM(210, 8) = 840
Final result: 840


Alternative Approach with Validation

const rangeLCMValidated = (arr) => {
    // Input validation
    if (!Array.isArray(arr) || arr.length !== 2) {
        throw new Error("Input must be an array of exactly 2 numbers");
    }
    
    const [start, end] = arr[0] 

60
660


Conclusion

Finding the LCM of a range requires iteratively calculating the LCM of each number with the running result. The key is using the mathematical relationship between GCD and LCM to efficiently compute the result.