Free LCM Calculator Online
Find the least common multiple of any set of numbers with this free LCM calculator. Enter your numbers separated by commas and get instant results with prime factorizations and step-by-step work.
Find the Least Common Multiple
Least Common Multiple
LCM(12, 18, 24) = 72
Prime Factorizations
Step-by-Step
How the LCM Calculator Works
This LCM calculator uses the relationship between LCM and GCF: LCM(a, b) = |a × b| / GCF(a, b). The GCF is found using the Euclidean algorithm, which is fast even for very large numbers. For more than two numbers, the LCM calculator chains the computation: LCM(a, b, c) = LCM(LCM(a, b), c). It also performs prime factorization on each input using trial division, so you can see exactly which primes contribute to the result. The LCM equals the product of all prime factors taken at their highest powers.
When You Need the LCM
The most common use of the least common multiple is adding or subtracting fractions with different denominators. To add 1/4 and 1/6, you need a common denominator: LCM(4, 6) = 12. Convert to 3/12 + 2/12 = 5/12. The LCM also appears in scheduling problems. If one bus arrives every 12 minutes and another every 18 minutes, they meet at the same stop every LCM(12, 18) = 36 minutes. This free LCM calculator handles both classroom problems and practical calculations.
LCM Examples
| Numbers | LCM | Method |
|---|---|---|
| 4, 6 | 12 | LCM = |4×6| / GCF(4,6) = 24/2 |
| 12, 18 | 36 | LCM = |12×18| / 6 = 216/6 |
| 8, 12, 15 | 120 | LCM(LCM(8,12),15) = LCM(24,15) |
| 3, 5, 7 | 105 | All coprime → 3×5×7 |
| 10, 25, 50 | 50 | 50 is already a multiple of 10 and 25 |
LCM Methods Compared
There are several approaches to finding the least common multiple. The right choice depends on how many numbers you have and how large they are.
GCF Method (Recommended)
LCM(a, b) = |a × b| / GCF(a, b). Fast, reliable, and the method this LCM calculator uses. Find the GCF with the Euclidean algorithm, then one division gives you the LCM.
Prime Factorization Method
Factor each number into primes. The LCM is the product of every prime factor raised to its highest power. LCM(12, 18): 12 = 2²×3, 18 = 2×3², LCM = 2²×3² = 36. More visual, and the LCM calculator shows these factorizations.
Listing Multiples
List multiples of each number until you find the first one they share. Multiples of 4: 4, 8, 12... Multiples of 6: 6, 12... LCM = 12. Simple for small numbers but slow for large ones.
Frequently Asked Questions
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