How to Calculate Lcm

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Least Common Multiple (LCM) Calculator

How to Calculate LCM

The Least Common Multiple (LCM) is the smallest positive integer that is perfectly divisible by a set of numbers without leaving a remainder. It is a fundamental concept in arithmetic and algebra, often used when adding or subtracting fractions with different denominators.

Method 1: Listing Multiples

This is the most straightforward method for small numbers. You list the multiples of each number until you find the first one they all share.

Example: Find LCM of 4 and 6
Multiples of 4: 4, 8, 12, 16, 20…
Multiples of 6: 6, 12, 18, 24…
LCM = 12 (The first number to appear in both lists).

Method 2: Prime Factorization

For larger numbers, prime factorization is more efficient. You break each number down into its prime factors and then multiply the highest power of every prime factor present in any of the numbers.

Example: Find LCM of 12 and 18
12 = 22 × 31
18 = 21 × 32
Highest power of 2: 22 = 4
Highest power of 3: 32 = 9
LCM = 4 × 9 = 36

Method 3: Using the GCD Formula

There is a specific mathematical relationship between the Greatest Common Divisor (GCD) and the LCM of two numbers:

LCM(a, b) = (a × b) / GCD(a, b)

function calculateLCMLogic() { var inputString = document.getElementById("numberInput").value; var resultArea = document.getElementById("lcm-result-area"); var resultText = document.getElementById("resultText"); // Clean input and convert to array of numbers var numberArray = inputString.split(/[\s,]+/).map(function(item) { return parseInt(item.trim(), 10); }).filter(function(item) { return !isNaN(item) && item !== 0; }); if (numberArray.length < 2) { resultArea.style.display = "block"; resultText.innerHTML = "Please enter at least two valid numbers."; return; } // GCD function using Euclidean Algorithm function findGCD(a, b) { a = Math.abs(a); b = Math.abs(b); while (b) { var temp = b; b = a % b; a = temp; } return a; } // LCM function for two numbers function findLCMTwoNumbers(a, b) { if (a === 0 || b === 0) return 0; return Math.abs(a * b) / findGCD(a, b); } // Calculate LCM for the entire array var runningLCM = numberArray[0]; for (var i = 1; i < numberArray.length; i++) { runningLCM = findLCMTwoNumbers(runningLCM, numberArray[i]); } // Display Result resultArea.style.display = "block"; resultText.innerHTML = "The Least Common Multiple (LCM) of " + numberArray.join(", ") + " is:" + runningLCM + ""; }

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