LCM Calculator — Least Common Multiple
Calculate the least common multiple (LCM) of two or more numbers. Also shows the prime factorization of each number. See also GCF Calculator and Fraction Calculator.
Enter at least 2 positive integers separated by commas
How to Find the LCM
The least common multiple (LCM) of two or more numbers is the smallest positive integer that is divisible by all of them. There are several methods to find the LCM: prime factorization (take the highest power of each prime), the formula LCM(a,b) = |a×b| / GCD(a,b), or listing multiples until you find a common one. This calculator uses the GCD method for efficiency and also shows the prime factorization of each input number.
LCM Formula
LCM(a, b) = |a × b| / GCD(a, b)
Using prime factorization:
LCM = product of highest powers of all primes
For multiple numbers:
LCM(a, b, c) = LCM(LCM(a, b), c)
Example
LCM(12, 18) = ?
12 = 2² × 3
18 = 2 × 3²
LCM = 2² × 3² = 4 × 9
= 36
Frequently Asked Questions
What is the difference between LCM and GCF?
LCM (Least Common Multiple) is the smallest number divisible by all given numbers. GCF (Greatest Common Factor) is the largest number that divides all given numbers. They are related: LCM(a,b) × GCF(a,b) = a × b.
When do you use LCM?
LCM is used when adding or subtracting fractions (finding a common denominator), scheduling problems (when events with different cycles align), and in number theory. For example, to add 1/4 + 1/6, you need LCM(4,6) = 12 as the common denominator.
Can LCM be calculated for more than 2 numbers?
Yes. Calculate LCM of the first two numbers, then find the LCM of that result with the third number, and so on. This calculator supports any number of inputs.
Is LCM always greater than or equal to the input numbers?
Yes. The LCM must be divisible by each input number, so it is always at least as large as the largest input. If one number is a multiple of the other, the LCM equals the larger number.