Find the least common multiple.
Enter any list of whole numbers to see their least common multiple, their greatest common divisor, and exactly how the LCM is built from prime factors.
Your numbers
Use positive whole numbers like 4, 6, 10. The LCM answers "when do these cycles line up again?"
What this means
Prime factorization breakdown
| Number | Prime factorization |
|---|
How LCM works
What Is the Least Common Multiple?
The LCM is the smallest positive number that is a multiple of two or more numbers. For example, LCM(12, 18) = 36, because 36 is the smallest number divisible by both 12 and 18. The LCM is essential for adding fractions with different denominators.
How to Find the LCM
Method 1: List multiples until you find a common one. Method 2: Use prime factorization, take the highest power of each prime factor. Method 3: Use the formula LCM(a,b) = |a×b| / GCF(a,b). This calculator shows the steps using prime factorization.
LCM Using Prime Factorization
Factor each number into primes. For each prime, take the highest power that appears. LCM(12,18): 12 = 2² × 3, 18 = 2 × 3². Take 2² and 3², so LCM = 4 × 9 = 36. This method works for any number of inputs.
LCM in Everyday Applications
LCM is used to find common denominators when adding fractions, schedule recurring events (two buses running on different schedules), synchronize cycles, and solve timing problems. It answers: "When will these two patterns coincide again?"
Common questions
What is the relationship between LCM and GCF?
For any two numbers a and b: LCM(a,b) × GCF(a,b) = a × b. This means if you know one, you can calculate the other. For example, LCM(12,18) × GCF(12,18) = 36 × 6 = 216 = 12 × 18.
Can the LCM be one of the numbers?
Yes. If one number is a multiple of the other, the LCM is the larger number. For example, LCM(4, 12) = 12, because 12 is already a multiple of 4.
What is the LCM of two prime numbers?
The LCM of two different prime numbers is always their product. For example, LCM(7, 11) = 77. Prime numbers have no common factors other than 1.
Can I find the LCM of more than two numbers?
Yes. Find the LCM of the first two, then find the LCM of that result with the third number, and so on. This calculator supports up to three numbers.
For positive whole numbers only. Zeros and non-integers are ignored, since the least common multiple is defined for positive integers.