least common denominator calculator javascript
AI Overview
To create a Least Common Denominator (LCD) calculator in JavaScript, one must first understand that the LCD of a set of fractions is equivalent to the Least Common Multiple (LCM) of their denominators. Therefore, the core of the calculator lies in implementing functions for the Greatest Common Divisor (GCD) and the LCM.
Here is a JavaScript implementation for calculating the LCD of multiple numbers (denominators):
JavaScript

// Function to calculate the Greatest Common Divisor (GCD) using the Euclidean algorithm
function gcd(a, b) {
if (b === 0) {
return a;
}
return gcd(b, a % b);
}

// Function to calculate the Least Common Multiple (LCM) of two numbers
function lcm(a, b) {
// LCM(a, b) = |a * b| / GCD(a, b)
return Math.abs(a * b) / gcd(a, b);
}

// Function to calculate the Least Common Denominator (LCD) for an array of numbers (denominators)
function calculateLCD(denominators) {
if (!Array.isArray(denominators) || denominators.length === 0) {
return null; // Handle invalid input
}

let resultLcm = denominators[0];
for (let i = 1; i < denominators.length; i++) {
resultLcm = lcm(resultLcm, denominators[i]);
}
return resultLcm;
}

// Example usage:
const denominators1 = [2, 3, 5];
const lcd1 = calculateLCD(denominators1);
console.log(`LCD of [${denominators1}] is: ${lcd1}`); // Output: LCD of [2,3,5] is: 30

const denominators2 = [6, 15, 10];
const lcd2 = calculateLCD(denominators2);
console.log(`LCD of [${denominators2}] is: ${lcd2}`); // Output: LCD of [6,15,10] is: 30

const denominators3 = [4, 8, 12];
const lcd3 = calculateLCD(denominators3);
console.log(`LCD of [${denominators3}] is: ${lcd3}`); // Output: LCD of [4,8,12] is: 24

Explanation:

gcd(a, b) function:
This function implements the Euclidean algorithm to find the greatest common divisor of two numbers a and b. It is a recursive function that continues dividing the larger number by the smaller number until the remainder is 0. The last non-zero remainder is the GCD.
lcm(a, b) function:
This function calculates the least common multiple of two numbers a and b using the formula: LCM(a, b) = |a * b| / GCD(a, b). Math.abs() is used to ensure a positive result.
calculateLCD(denominators) function:
This function takes an array of denominators as input. It initializes resultLcm with the first denominator and then iteratively calculates the LCM of resultLcm and each subsequent denominator in the array. This effectively finds the LCM of all denominators, which is the LCD. It also includes basic input validation.