LCM Calculator
Find the least common multiple of two positive whole numbers quickly and accurately with our free LCM Calculator.
Enter two numbers to calculate their LCM and see the multiples and calculation details behind the result.
Calculate the LCM
Enter two positive whole numbers below.
LCM Result
What Is the Least Common Multiple?
The least common multiple (LCM) of two positive whole numbers is the smallest positive number that is a multiple of both numbers.
For example, the multiples of 4 include 4, 8, 12, 16, 20, and so on. The multiples of 6 include 6, 12, 18, 24, and so on.
The first positive number that appears in both lists is 12, so the LCM of 4 and 6 is 12.
Example: LCM of 4 and 6
The multiples of 4 are:
4, 8, 12, 16, 20, 24...
The multiples of 6 are:
6, 12, 18, 24, 30...
The first positive multiple shared by both lists is 12.
Therefore:
LCM(4, 6) = 12
LCM Formula Using GCD
The LCM of two positive integers can also be calculated using their greatest common divisor (GCD).
LCM(a, b) = |a × b| ÷ GCD(a, b)
For example, consider 12 and 18.
The GCD of 12 and 18 is 6.
Therefore:
LCM(12, 18) = (12 × 18) ÷ 6 = 36
Common LCM Examples
| First Number | Second Number | LCM |
|---|---|---|
| 2 | 3 | 6 |
| 4 | 6 | 12 |
| 5 | 10 | 10 |
| 6 | 8 | 24 |
| 8 | 12 | 24 |
| 9 | 15 | 45 |
| 12 | 18 | 36 |
| 15 | 20 | 60 |
How to Use the LCM Calculator
- Enter the first positive whole number.
- Enter the second positive whole number.
- Click Calculate LCM.
- Review the LCM and calculation details.
- Click Reset to perform another calculation.
When Is LCM Useful?
The least common multiple is useful whenever repeating schedules, cycles, or groups need to line up at the same point.
For example, if one event happens every 4 days and another happens every 6 days, their schedules will coincide again after 12 days, assuming they start together.
LCM is also commonly used when working with fractions, multiples, number patterns, and other mathematical problems.
Frequently Asked Questions
What does LCM stand for?
LCM stands for Least Common Multiple.
What is the LCM of 4 and 6?
The LCM of 4 and 6 is 12 because 12 is the smallest positive number divisible by both 4 and 6.
What is the LCM of 12 and 18?
The LCM of 12 and 18 is 36.
Can the LCM be the same as one of the numbers?
Yes. If one number is already a multiple of the other, the larger number is the LCM. For example, the LCM of 5 and 10 is 10.
What is the difference between LCM and GCD?
The LCM is the smallest positive number that is a multiple of both numbers, while the GCD is the largest positive number that divides both numbers evenly.