LCM Calculator - Least Common Multiple
Welcome to our free LCM calculator! This simple and easy-to-use tool helps you find the Least Common Multiple (LCM) of two or more numbers in seconds. Whether you’re a student trying to understand how to calculate LCM for a math problem or need a quick and accurate answer for adding fractions or solving scheduling problems, our calculator is here to help.
LCM Calculator
Find the Least Common Multiple (LCM) of two or more numbers.
The Least Common Multiple (LCM) is:
120
Solving Steps (Prime Factorization)
What is the Least Common Multiple (LCM)?
The Least Common Multiple (LCM) of a set of integers is the smallest positive integer that is evenly divisible by all the numbers in that set. In other words, it’s the smallest “common multiple” they all share.
For example, to find the LCM of 4 and 6:
Multiples of 4 are: 4, 8, 12, 16, 20, 24, …
Multiples of 6 are: 6, 12, 18, 24, …
The common multiples are 12, 24, and so on. The least (smallest) of these is 12. Therefore, the LCM of 4 and 6 is 12.
Our lcm calculator – least common multiple tool automates this process, saving you time and preventing errors, especially with larger or more numerous values.
How to Calculate LCM Manually
If you need to know how to calculate LCM by hand, there are several common methods. Our calculator uses an advanced version of the Prime Factorization method to show you the steps.
The Listing Multiples Method
This is the method used in the example above. You list out the multiples of each number until you find the first one that appears in all lists. This is simple for small numbers but becomes very difficult for larger numbers.
The Prime Factorization Method
This is the most reliable manual method and the one our calculator demonstrates.
Find the prime factors of each number in your set.
List all prime factors that appear in any of the factorizations.
Find the highest power (highest exponent) of each prime factor from any of the sets.
Multiply these highest powers together to get the LCM.
Example: Find the LCM of 12, 15, and 20
Step 1 (Factor):
12 = 2 × 2 = 2²
15 = 3 × 5 = 3¹ × 5¹
20 = 2 × 2 × 5 = 2² × 5¹
Step 2 & 3 (Highest Powers):
The highest power of 2 is 2² (from 12 and 20).
The highest power of 3 is 3¹ (from 15).
The highest power of 5 is 5¹ (from 15 and 20).
Step 4 (Multiply):
LCM = 2² × 3¹ × 5¹ = 4 × 3 × 5 = 60
The GCF (Greatest Common Factor) Method
For two numbers, ‘a’ and ‘b’, you can use a special formula involving their Greatest Common Factor (GCF).
Formula:
LCM(a, b) = (|a × b|) / GCF(a, b)
This method is fast for two numbers but gets complicated when you add more.
How to Use Our Calculator LCM Tool
Why struggle with manual calculations? Our calculator lcm tool makes finding the least common multiple effortless.
- Enter Your Numbers: Type your numbers (like 12, 15, 20) into the input box. You can separate them with commas or spaces.
- Click Calculate: Hit the “Calculate LCM” button.
- Get Your Answer: The lcm of calculator will instantly show you the correct LCM. It will also provide a detailed, step-by-step breakdown using the Prime Factorization method, so you can learn exactly how the answer was found.