LCM Calculator

Enter a set of numbers and calculate their least common multiple.

Least Common Multiple Calculator

Result

What is the Least Common Multiple (LCM)?

The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all the numbers in a given set. The LCM is often used in mathematics to solve fraction problems, scheduling, and other similar tasks.

How to Calculate the Least Common Multiple?

You can calculate the LCM of a set of numbers using the following two methods:

1. Listing Method

Steps:

List the multiples of each number.
Identify the common multiples.
Choose the smallest common multiple as the LCM.

Example: Find the LCM of 4 and 6.

Solution:

Multiples of 4: 4, 8, 12, 16, 20, ...

Multiples of 6: 6, 12, 18, 24, ...

Common multiples: 12, 24, ...

LCM: 12

2. Using the Greatest Common Divisor (GCD)

Steps:

Find the GCD of the two numbers.
Use the following formula to calculate the LCM: \( \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \)

Example: Find the LCM of 15 and 25.

Solution:

1. First, calculate the GCD:

Factors of 15: 1, 3, 5, 15

Factors of 25: 1, 5, 25

Common factors: 1, 5

So, the GCD of 15 and 25 is 5.

2. Calculate the LCM:

\( \text{LCM}(15, 25) = \frac{15 \times 25}{5} = 75 \)

So, the LCM of 15 and 25 is 75.

Input Format

You can input your numbers separated by commas or line breaks. The calculator also automatically handles spaces, semicolons, and other delimiters, whether they are used singly or in combination.

Examples:

Comma-separated: 4, 6

Semicolon-separated: 12; 15; 20

Comma and space-separated: 5, 10 15 20, 40

Comma, semicolon, and space-separated: 10, 20; 35 50, 100 200; 500