1
Find the GCF
Use the Euclidean algorithm to find the greatest common factor of the first two integers.
LCM
LCM Calculator
Find the least common multiple of two or more integers with exact results, GCF, prime factorization, and step-by-step calculations.
Exact BigInt Results
LCM & GCF
Calculation Steps
×
Enter Integers
Enter 2–50 whole numbers separated by commas, spaces, semicolons, or new lines. Negative integers and zero are supported.
Try an example
GCF method steps
- 1. LCM(330, 75) = (330 ÷ 15) × 75 = 1,650
- 2. LCM(1,650, 450) = (1,650 ÷ 150) × 450 = 4,950
- 3. LCM(4,950, 225) = (4,950 ÷ 225) × 225 = 4,950
=
Live Results
Least common multiple
4,950
GCF / GCD
15
Number count
4
Largest input
450
LCM digits
4
Prime factorization
- 330 = 2 × 3 × 5 × 11
- 75 = 3 × 5^2
- 450 = 2 × 3^2 × 5^2
- 225 = 3^2 × 5^2
Highest required prime powers give LCM = 4,950.
Tip: the LCM is always non-negative. If any input is 0, the LCM of the list is 0.
∑ How to Calculate LCM
The least common multiple is the smallest positive integer divisible by every number in the set. For two non-zero integers, the fastest manual formula uses their greatest common factor.
LCM(a, b) = |a × b| ÷ GCF(a, b)
2
Divide, then multiply
Divide one integer by the GCF before multiplying by the other. This produces their LCM.
3
Repeat for the list
Use the result with the next integer and continue until every input has been included.
Worked example: LCM of 18 and 26
GCF(18, 26) = 2, so LCM(18, 26) = (18 ÷ 2) × 26 = 234.
≡ Calculator of LCM Methods
There are three common ways to calculate the LCM. They produce the same answer, but each is useful in a different situation.
Listing multiples
12: 12, 24, 36…
List multiples of each number until the first shared value appears. It is intuitive for small integers but becomes slow quickly.
Prime factorization
LCM = product of highest prime powers
Factor each integer and select the greatest exponent of every prime. This clearly shows why the result is divisible by all inputs.
GCF / GCD method
LCM(a,b) = |a×b| ÷ GCF(a,b)
Use the Euclidean algorithm for the GCF, then apply the product formula pairwise. This is efficient even for large integers.
✓ Least Common Multiple Examples
| Numbers | GCF | LCM | Check |
|---|---|---|---|
| 8, 12 | 4 | 24 | 24 ÷ 8 = 3; 24 ÷ 12 = 2 |
| 18, 26 | 2 | 234 | 234 ÷ 18 = 13; 234 ÷ 26 = 9 |
| 21, 14, 38 | 1 | 798 | 798 is divisible by all three |
| 4, 6, 8 | 2 | 24 | 24 is the first shared multiple |
When Is an LCM Calculator Useful?
Common denominators
Find the least common denominator needed to add or subtract fractions.
Repeating schedules
Determine when events with different repeat intervals occur together again.
Cycles and rotations
Align machine cycles, gear rotations, signals, or periodic processes.
Grouping problems
Find the smallest quantity that can be arranged evenly into several group sizes.
? LCM Calculator FAQ
What is the least common multiple?
The least common multiple (LCM) is the smallest positive integer divisible by every number in a set. For example, the LCM of 4 and 6 is 12.
How do you calculate LCM?
Find the GCF of two numbers, divide one number by the GCF, then multiply by the other number: LCM(a,b) = |a × b| ÷ GCF(a,b). Repeat pairwise for more than two numbers.
How do I calculate the LCM by prime factorization?
Write each number as a product of primes. Take every prime that appears, using its highest exponent, then multiply those prime powers. For 12 = 2²×3 and 18 = 2×3², LCM = 2²×3² = 36.
How do I find the LCM of three or more numbers?
Calculate pairwise: first find LCM(a,b), then find the LCM of that result and c. Continue until every number has been included. The order does not change the final result.
What is the difference between LCM and GCF?
The LCM is the smallest positive shared multiple, while the GCF or GCD is the largest positive shared divisor. For two non-zero integers, LCM × GCF = |a × b|.
What is the LCM of 0 and a number?
The LCM of 0 and any integer is 0, because there is no positive multiple of 0. The calculator follows this standard convention.
Can an LCM calculator use negative numbers?
Yes. Divisibility and multiples are determined from absolute values, so LCM(−4, 6) is the same as LCM(4, 6), which is 12.
Can I calculate the LCM of decimals or fractions?
LCM is normally defined for integers. Convert decimals or fractions to whole-number ratios first, or clear their denominators before calculating the integer LCM.
What is a calculator of LCM used for?
A calculator of LCM quickly finds when repeating intervals align, creates common denominators for fractions, and solves grouping or scheduling problems involving multiple cycles.
Can this LCM of calculator handle very large integers?
Yes. This LCM of calculator uses exact BigInt arithmetic for inputs up to 100 digits, so results do not lose precision like ordinary floating-point calculations.
How is LCM used to add fractions?
Find the LCM of the denominators and use it as the least common denominator. Convert each fraction to that denominator, then add or subtract the numerators.
Is the LCM always larger than the input numbers?
When every input is non-zero, the LCM is at least as large as the largest absolute input, but it may equal one input when all other numbers divide it exactly. For example, LCM(4, 8) = 8. If any input is zero, the LCM is zero.
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