LCM Calculator

Calculate the Least Common Multiple (LCM) of a set of numbers.

Calculator

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Enter numbers separated by commas (e.g., 12, 18, 24)

Table of Contents

1 LCM Formula
2 How to Calculate LCM
3 LCM - Practical Examples
Concept

LCM Formula

The Least Common Multiple (LCM) of two or more numbers is the smallest positive integer that is divisible by all the numbers.

Formula:
LCM(a,b) = |a × b| / GCD(a,b)
Steps

How to Calculate LCM

To calculate the LCM, follow these steps:

  1. 1
    Find the prime factorization of each number
  2. 2
    Take the highest power of each prime factor
  3. 3
    Multiply these prime factors together

For example, to find the LCM of 12 and 18:

Example Calculation:
12 = 2² × 3
18 = 2 × 3²
LCM = 2² × 3² = 36
Examples

LCM - Practical Examples

Example 1 Finding Common Time Intervals

Two trains leave a station at intervals of 12 and 18 minutes. When will they leave together again?

LCM(12, 18) = 36 minutes

Example 2 Package Sizes

A store sells items in packages of 8, 12, and 16. What is the smallest number of items that can be bought in equal packages?

LCM(8, 12, 16) = 48 items

Example 3 Recurring Events

Three events occur every 4, 6, and 8 days. When will all three events occur on the same day?

LCM(4, 6, 8) = 24 days

Tools

Mathematics Calculators

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