Math
LCM Calculator (Least Common Multiple)
Find the least common multiple of two or more numbers. Includes step-by-step calculation and prime factorizations.
Enter numbers
Enter at least two positive integers.
Least Common Multiple
24
Step-by-step
- Start with 4.
- lcm(4, 6) = 12
- lcm(12, 8) = 24
Prime factorization
- 4 = 2 x 2
- 6 = 2 x 3
- 8 = 2 x 2 x 2
Frequently Asked Questions about the LCM Calculator (Least Common Multiple)
What is the least common multiple (LCM)?
The LCM is the smallest positive integer that is evenly divisible by every number in a set. For 4 and 6, the LCM is 12 - the first multiple that both 4 and 6 divide into with no remainder.
How do I find the LCM by hand?
Two reliable methods: list multiples of each number until you find the first one they share, or use prime factorization. With prime factorization, write each number as a product of prime powers, then multiply the highest power of each prime that appears across all inputs. For example, 4 = 2^2 and 6 = 2 x 3, so LCM = 2^2 x 3 = 12.
What is the LCM of 4 and 6?
12. Multiples of 4: 4, 8, 12 ... Multiples of 6: 6, 12 ... The first shared value is 12. You can verify: 12 / 4 = 3 and 12 / 6 = 2, both whole numbers.
How is LCM related to GCF?
For any two positive integers a and b: LCM(a, b) x GCF(a, b) = a x b. So if you know the GCF you can find the LCM with a single division, and vice versa. For 4 and 6: GCF = 2, so LCM = (4 x 6) / 2 = 12.
Why do I need LCM?
LCM is most commonly used to find a common denominator when adding or subtracting fractions with different denominators. It also appears in scheduling problems - if two events repeat every 4 days and every 6 days, they next coincide in 12 days - and in number theory and cryptography.
Can I find the LCM of more than two numbers?
Yes. The calculator reduces pairwise: LCM(a, b, c) = LCM(LCM(a, b), c). Enter as many integers as you need, separated by commas or spaces, and the result updates automatically.
What is the LCM of 0 and any number?
Zero has no useful LCM with another number, so this calculator skips any zeros in your input. If only zeros are entered, or just one non-zero number remains after filtering, the calculator returns no result because at least two valid integers are required.