Find a common denominator
Use the LCM when rewriting fractions like 3/4 and 5/6 with the same denominator before combining them.
LCM(4, 6) = 12
You can rewrite the fractions as 9/12 and 10/12.
Least Common Multiple Calculator
Use this calculator to find the least common multiple (LCM) of two or more numbers. Get step-by-step solutions and understand how LCM is calculated.
Least Common Multiple Calculator
Enter two or more numbers separated by commas, then click Calculate to find their least common multiple (LCM).
Result
What is the Least Common Multiple (LCM)?
The Least Common Multiple (LCM) of two or more numbers is the smallest positive number that is divisible by all of them without a remainder.
For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 can divide into evenly.
Methods to Find the LCM
Prime Factorization Method
This method involves finding the prime factorization of each number, then multiplying the highest power of each prime factor that appears in any of the numbers.
Example: To find LCM(12, 18) 1. Prime factorization: 12 = 2² × 3, 18 = 2 × 3² 2. Take the highest power of each prime factor: 2² and 3² 3. Multiply them: 2² × 3² = 4 × 9 = 36 Therefore, LCM(12, 18) = 36
Using the GCD/GCF Method
The LCM can also be calculated using the relationship between LCM and GCD (Greatest Common Divisor):
LCM(a, b) = (a × b) ÷ GCD(a, b)
Example: To find LCM(12, 18) 1. Find GCD(12, 18) = 6 2. Calculate: (12 × 18) ÷ 6 = 216 ÷ 6 = 36 Therefore, LCM(12, 18) = 36
Applications of LCM
- Finding common time periods (e.g., when two events will coincide again)
- Working with fractions (finding common denominators)
- Solving scheduling and synchronization problems
- Optimizing resource allocation in computer science
How to Use This Calculator
- Enter two or more positive integers separated by commas in the input field.
- Click the 'Calculate' button to find the LCM.
- View the result and the step-by-step solution explaining how the LCM was calculated.
- Click 'Clear' to reset the calculator and perform a new calculation.
Use whole numbers only. If you need to compare denominators before adding or subtracting fractions, the LCM shown here can also serve as the least common denominator.
LCM Examples
Compare repeating schedules
The LCM helps identify when recurring events line up again, such as alarms every 8 minutes and 12 minutes.
LCM(8, 12) = 24
The two events happen together every 24 minutes.
Evaluate three values at once
You can enter more than two numbers to find the first shared multiple across several quantities.
LCM(12, 18, 30) = 180
180 is the smallest positive number divisible by all three.
Least Common Multiple FAQ
What is the difference between LCM and GCD?
The least common multiple is the smallest positive number shared by all inputs, while the greatest common divisor is the largest number that divides each input exactly.
Can the LCM calculator handle more than two numbers?
Yes. Enter multiple positive integers separated by commas and the calculator will evaluate them together to find one common multiple.
Why is LCM useful for fractions?
When fractions have different denominators, the LCM gives you the smallest common denominator, which keeps the rewritten fractions simpler.
Do negative numbers change the LCM?
This calculator accepts positive integers because LCM is typically expressed as the smallest positive common multiple.