Least Common Multiple Calculator

Find the least common multiple of two or more integers quickly and accurately.

▼ Enter numbers separated by commas and click Calculate

Numbers

Least Common Multiple —

What Is the Least Common Multiple (LCM)?

The least common multiple (LCM), also known as the lowest common multiple, is the smallest positive integer that is divisible by two or more integers without leaving a remainder.

Example:
LCM(12, 18) = 36

Another example:
LCM(8, 20) = 40

The LCM is commonly used when working with fractions, repeating schedules, and problems where several numbers need to share a common multiple.

Brute Force Method

One basic way to find the least common multiple is to list the multiples of each number until a common multiple is found. The smallest common multiple is the LCM.

Example:
Multiples of 12: 12, 24, 36, 48, 60, ...
Multiples of 18: 18, 36, 54, 72, ...
Therefore, LCM(12, 18) = 36

This method is easy to understand, but it can become tedious when working with larger numbers.

Prime Factorization Method

Another systematic way to find the LCM is to use prime factorization. Break each number into its prime factors, then multiply the highest power of each prime that appears in any of the numbers.

Example:
12 = 2 × 2 × 3
18 = 2 × 3 × 3
LCM(12, 18) = 2 × 2 × 3 × 3 = 36

This method is more systematic than listing multiples, although prime factorization can still become difficult for very large numbers.

GCF Method

The LCM of two numbers can also be found using their greatest common factor (GCF). Multiply the two numbers together and divide the product by their GCF.

Formula:
LCM(a, b) = (a × b) / GCF(a, b)

Example:
GCF(12, 18) = 6
LCM(12, 18) = (12 × 18) / 6 = 36

For more than two numbers, calculate the LCM of two numbers first, then use that result with the next number until all the numbers have been included.

How to Use the LCM Calculator

Step 1: Enter two or more integers separated by commas.

Step 2: Click the Calculate button.

Step 3: The calculator finds and displays the least common multiple of all the numbers entered.

Frequently Asked Questions

What is the least common multiple?

The least common multiple (LCM) is the smallest positive integer that is divisible by two or more integers without leaving a remainder.

How many numbers can I enter?

You can enter two or more integers separated by commas. The calculator finds the LCM across all the numbers entered.

Can I enter negative numbers?

Yes. The calculator accepts negative integers and uses their absolute values when calculating the LCM.

What happens if I enter zero?

If any of the entered numbers is zero, the calculator displays an LCM of 0.

What is the difference between LCM and GCF?

The LCM is the smallest positive number divisible by all the given integers, while the GCF is the largest positive number that divides all the given integers.

Can I find the LCM of more than two numbers?

Yes. Enter all the integers separated by commas and the calculator will find the LCM of all of them.

Disclaimer

This calculator is provided for general mathematical and educational purposes. While we aim to provide accurate results, SmartMyTools does not guarantee that the results are suitable for professional, academic, financial, engineering, or other specialized applications.