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 two or more numbers all divide into evenly. For 4 and 6, the LCM is 12 because 12 is the first number that both 4 and 6 fit into without a 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 (multiply the highest power of each prime that appears across all inputs).
What is the LCM of 4 and 6?
12. Multiples of 4: 4, 8, 12, 16; multiples of 6: 6, 12, 18. The first common multiple is 12.
How is LCM related to GCF?
For any two positive integers a and b: LCM(a, b) x GCF(a, b) = a x b. This means you can compute one from the other.
Why do I need LCM?
LCM is essential for adding or subtracting fractions with different denominators, scheduling cycles (every 4 days and every 6 days coincide every 12), and solving problems in number theory.
Can I find the LCM of more than two numbers?
Yes. Compute it pairwise: LCM(a, b, c) = LCM(LCM(a, b), c). Enter as many numbers as you want, separated by commas or spaces.
What is the LCM of 0 and any number?
Strictly, the LCM of 0 and any non-zero number is 0. This calculator ignores zeros in the input because they make the LCM trivial.