Least Common Multiple (LCM) Calculator
User Inputs
The LCM Calculations
How this LCM Calculator works?
Find the Least Common Multiple (LCM) of multiple integers instantly with this fast and interactive calculator. This tool computes the LCM using two standard mathematical methods, helping you understand the process step by step:
- Prime Factorization Method - Break each number into its prime factors and combine the highest powers.
- Division Method (Ladder Method) - Divide the numbers simultaneously using common prime factors.
Simply enter your numbers in the input field above. You can separate values using spaces or commas, and the result updates in real time as you type.
Each calculation is presented in a clear, structured format so you can follow the logic easily — ideal for both learning and quick problem solving.
You can also save and share your LCM calculation as a unique link, making it useful for homework, classroom discussion, or collaboration.
Key Features of This LCM Calculator
- Instant real-time calculation
- Step-by-step solutions for both methods
- Accepts comma or space-separated inputs
- Shareable calculation links
- Works seamlessly across devices
- Designed for students, teachers, and quick practice
Calculation Examples Using Prime Factorization Method
1. Finding LCM for 4 and 12
In the Prime Factorization method, each number is expressed as a product of its prime factors. The LCM is obtained by taking all prime factors with their highest powers (exponents).
4 and 12
The Prime Factors of 4
4=2✕2=22The Prime Factors of 12
12=2✕2✕3=22✕3
Take only the highest powers (exponents) for each of the Prime Factor from the above.
22 and
3
The LCM is the product of the these Prime Factors with highest powers (exponents).
The LCM(4, 12) is:
=22✕3
=2✕2✕3
=12
2. Finding LCM for 5, 15, 20 and 22
In the Prime Factorization method, each number is expressed as a product of its prime factors. The LCM is obtained by taking all prime factors with their highest powers (exponents).
5, 15, 20 and 22
The Prime Factors of 5
5 (as 5 is already a prime number)The Prime Factors of 15
15=3✕5The Prime Factors of 20
20=2✕2✕5=22✕5The Prime Factors of 22
22=2✕11
Take only the highest powers (exponents) for each of the Prime Factor from the above.
22,
3,
5 and
11
The LCM is the product of the these Prime Factors with highest powers (exponents).
The LCM(5, 15, 20, 22) is:
=22✕3✕5✕11
=2✕2✕3✕5✕11
=660
Calculation Examples Using Division Method
1. Finding LCM for 10, 9 and 12
The division method is a systematic way to find the LCM by dividing the numbers by common prime factors.
10, 9 and 12
| 2 | 10 | 9 | 12 |
| 2 | 5 | 9 | 6 |
| 3 | 5 | 9 | 3 |
| 3 | 5 | 3 | 1 |
| 5 | 5 | 1 | 1 |
| 1 | 1 | 1 |
The LCM is the product of all the Prime Numbers in the 1st column of the above table.
The LCM(10, 9, 12) is:
=2✕2✕3✕3✕5
=180
2. Finding LCM for 15, 24, 26, 30 and 32
The division method is a systematic way to find the LCM by dividing the numbers by common prime factors.
15, 24, 26, 30 and 32
| 2 | 15 | 24 | 26 | 30 | 32 |
| 2 | 15 | 12 | 13 | 15 | 16 |
| 2 | 15 | 6 | 13 | 15 | 8 |
| 2 | 15 | 3 | 13 | 15 | 4 |
| 2 | 15 | 3 | 13 | 15 | 2 |
| 3 | 15 | 3 | 13 | 15 | 1 |
| 5 | 5 | 1 | 13 | 5 | 1 |
| 13 | 1 | 1 | 13 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 |
The LCM is the product of all the Prime Numbers in the 1st column of the above table.
The LCM(15, 24, 26, 30, 32) is:
=2✕2✕2✕2✕2✕3✕5✕13
=6240