Least Common Multiple Calculator
Find the least common multiple (LCM) of two or more positive integers. Enter your numbers and click Calculate — each step shows the GCD used and the resulting LCM.
Notes
What Is the Least Common Multiple?
The least common multiple (LCM) of two or more integers is the smallest positive integer that is divisible by all of them. It is also called the lowest common multiple or smallest common multiple.
How LCM Is Calculated
The most efficient method uses the relationship between LCM and GCD:
- Find GCD(a, b) using the Euclidean algorithm.
- Compute LCM(a, b) = (a × b) ÷ GCD(a, b).
- For more than two numbers, apply pairwise: LCM(a, b, c) = LCM(LCM(a, b), c).
Quick Example
LCM(12, 18): GCD(12, 18) = 6 → LCM = (12 × 18) ÷ 6 = 216 ÷ 6 = 36.
- How LCM works — full explanation — LCM methods, prime factorization approach, and applications
- LCM formula reference — Formula, variables, and worked examples
Frequently Asked Questions
What is LCM used for?
LCM is used to add and subtract fractions with different denominators (find the lowest common denominator), solve scheduling problems (when two events next coincide), and in music theory (finding rhythmic cycles).
What is LCM(a, b) × GCD(a, b) equal to?
LCM(a, b) × GCD(a, b) = a × b. This identity is always true for positive integers. It means knowing GCD lets you find LCM without prime factorization.
What is the LCM of two coprime numbers?
If GCD(a, b) = 1 (coprime), then LCM(a, b) = a × b. For example, LCM(8, 15) = 8 × 15 = 120, because GCD(8, 15) = 1.
Can LCM be smaller than the larger number?
No. LCM(a, b) ≥ max(a, b). The LCM equals the larger number only when one number divides the other. For example, LCM(6, 18) = 18, because 6 divides 18.
How do I find LCM using prime factorization?
Write each number as a product of prime powers. For each prime, take the highest exponent across all numbers. Multiply the results. Example: LCM(12, 18) — 12 = 2² × 3, 18 = 2 × 3². LCM = 2² × 3² = 4 × 9 = 36.