Greatest Common Factor (GCF) Calculator
Find the GCF and LCM of 2-4 numbers using the Euclidean algorithm and prime factorization. View step-by-step solutions, Bézout coefficients, and factor comparison visuals.
Least Common Multiple (LCM) Calculator
Calculate the LCM (Least Common Multiple) of 2–4 numbers using prime factorization. Also shows GCF, LCM×GCF relationship, prime factor breakdown, and multiples comparison table.
LCM (Least Common Multiple)⧉
36.00
The smallest positive integer divisible by all inputs: 12, 18
GCF (Greatest Common Factor)⧉
6.00
The largest positive integer that divides all inputs evenly
Product of Numbers⧉
216.00
12 × 18
LCM × GCF⧉
216.00
For two numbers: LCM × GCF = 12 × 18 = 216 ✓
LCM Prime Factorization⧉
2^2 × 3^2
Take the highest power of each prime across all numbers
GCF Prime Factorization⧉
2 × 3
Take the lowest power of each prime common to all numbers
Ratio LCM / GCF⧉
6.0000
How many times larger the LCM is compared to the GCF
Number Composition (Prime Factors)
122^2 × 3
2^2
3
182 × 3^2
2
3^2
Prime Factorization Breakdown
| Prime | 12 | 18 | LCM (max) | GCF (min) |
|---|---|---|---|---|
| 2 | 2 | 1 | 2 | 1 |
| 3 | 1 | 2 | 2 | 1 |
First Multiples Comparison
| k | 12 × k | 18 × k |
|---|---|---|
| 1 | 12.00 | 18.00 |
| 2 | 24.00 | 36.00 |
| 3 | 36.00 | 54.00 |
| 4 | 48.00 | 72.00 |
| 5 | 60.00 | 90.00 |
| 6 | 72.00 | 108.00 |
| 7 | 84.00 | 126.00 |
| 8 | 96.00 | 144.00 |
| 9 | 108.00 | 162.00 |
| 10 | 120.00 | 180.00 |
| 11 | 132.00 | 198.00 |
| 12 | 144.00 | 216.00 |
Planning notes, formulas, and examples
About the Least Common Multiple (LCM) Calculator
The Least Common Multiple (LCM) is the smallest positive integer that is evenly divisible by two or more numbers. Our LCM calculator finds the LCM of up to four numbers simultaneously, using the prime factorization method for fast, exact results. It also computes the Greatest Common Factor (GCF) and demonstrates the elegant relationship LCM(a, b) × GCF(a, b) = a × b for any pair of positive integers.
Finding the LCM is a fundamental skill in arithmetic and algebra, used every time you add or subtract fractions with different denominators, schedule repeating events, or solve problems involving modular arithmetic and number theory. Engineers use it for gear-tooth calculations, signal processing, and synchronization problems; teachers test it on every standardized math exam from grade school through college.
This calculator breaks down each number into its prime factors, highlights which prime powers are taken for the LCM (maximum exponents) versus the GCF (minimum exponents), and shows a multiples comparison table so you can visually confirm the answer. Colour-coded composition bars let you see at a glance how each input number is built from primes, making this an excellent learning and teaching tool as well as a quick computation aid.
When This Page Helps
Least Common Multiple (LCM) Calculator helps you solve least common multiple (lcm) problems quickly while keeping each step transparent. Instead of redoing long algebra by hand, you can enter Number A, Number B, Number C (optional) once and immediately inspect LCM (Least Common Multiple), GCF (Greatest Common Factor), Product of Numbers to validate your work.
How to Use the Inputs
- Enter Number A and Number B in the input fields.
- Select the mode, method, or precision options that match your least common multiple (lcm) problem.
- Read LCM (Least Common Multiple) first, then use GCF (Greatest Common Factor) to confirm your setup is correct.
- Try a preset such as "12, 18" to test a known case quickly.
Formula used
LCM(a, b) = |a × b| / GCF(a, b). Equivalently, factor each number into primes and take the highest power of every prime that appears. GCF uses the lowest power of each common prime.Example Calculation
Result: LCM (Least Common Multiple) shown by the calculator
Using the preset "12, 18", the calculator evaluates the least common multiple (lcm) setup, applies the selected algebra rules, and reports LCM (Least Common Multiple) with supporting checks so you can verify each transformation.
Tips & Best Practices
- If two numbers are coprime (GCF = 1), their LCM equals their product.
- LCM(a, b, c) = LCM(LCM(a, b), c) — you can compute it iteratively for any number of inputs.
- For fractions: LCD (Least Common Denominator) is just the LCM of the denominators.
- The LCM is always ≥ the largest input number and ≤ the product of all inputs.
How This Least Common Multiple (LCM) Calculator Works
This calculator takes Number A, Number B, Number C (optional), Number D (optional) and applies the relevant least common multiple (lcm) relationships from your chosen method. It returns both final and intermediate values so you can audit the process instead of treating it as a black box.
Interpreting Results
Start with the primary output, then use LCM (Least Common Multiple), GCF (Greatest Common Factor), Product of Numbers, LCM × GCF to confirm signs, magnitude, and internal consistency. If anything looks off, change one input and compare the updated outputs to isolate the issue quickly.
Study Strategy
Sources & Methodology
Last updated:
Frequently Asked Questions
LCM (Least Common Multiple) is the smallest number divisible by all inputs. GCF (Greatest Common Factor) is the largest number that divides all inputs evenly. They are related by LCM × GCF = a × b for two numbers.
This is a common misnomer — the correct term is Least Common Multiple (LCM). However, many people search for "least common factor," so we address both terms. The least common factor of any integer greater than 1 is technically just 1 (the smallest factor).
Find the LCM of the first two numbers, then find the LCM of that result with the third number. Alternatively, factor all three numbers into primes and take the maximum exponent of each prime.
Common uses include finding the least common denominator for fraction arithmetic, scheduling repeating events (e.g., alarms or shifts), gear ratio calculations, and synchronization in computing.
The LCM of two distinct primes is simply their product, since primes share no common factors other than 1.
No. The LCM is always at least as large as the largest input, because it must be a multiple of every input number.
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