Least Common Multiple Calculator
Find the least common multiple (LCM) of two or more numbers quickly and easily. Enter up to 10 numbers and get the LCM with step-by-step calculations and prime factorization.
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Quick Examples:
Methods to Find LCM
1. Prime Factorization Method
Find the prime factorization of each number, then take the highest power of each prime factor.
2. Division Method
Divide the numbers by their common factors until no common factors remain, then multiply all divisors and remaining numbers.
3. Listing Multiples Method
List the multiples of each number and find the smallest common multiple.
How to Use This Calculator
Applications of LCM
Real-World Applications
- Scheduling recurring events
- Finding common denominators in fractions
- Synchronizing periodic processes
- Planning production cycles
- Calculating gear ratios
- Determining meeting frequencies
Mathematical Applications
- Adding and subtracting fractions
- Solving Diophantine equations
- Number theory problems
- Modular arithmetic
- Cryptography algorithms
- Computer science algorithms
Example Calculations
Example 1: Two Numbers
Find LCM(24, 36):
Example 2: Three Numbers
Find LCM(12, 15, 20):
Example 3: Prime Numbers
Find LCM(7, 11, 13):
Frequently Asked Questions
What is the difference between LCM and GCD?
LCM (Least Common Multiple) is the smallest positive number that is divisible by all given numbers, while GCD (Greatest Common Divisor) is the largest number that divides all given numbers.
Can LCM be smaller than the largest input number?
No, the LCM is always greater than or equal to the largest input number. It equals the largest number only when that number is divisible by all other input numbers.
What happens with prime numbers?
When finding the LCM of prime numbers, the result is simply their product since prime numbers have no common factors other than 1.