Find the Least Common Denominator (LCD) and Least Common Multiple (LCM) for two or more fractions. Features prime factor trees, listing multiples, and proportional fraction scaling.
The Least Common Denominator (LCD) is the smallest positive integer that is divisible by all denominators in a collection of fractions. It represents the Least Common Multiple (LCM) of the denominators:
Input numerators and denominators for 2 or more fractions.
Decompose each denominator into its prime factor representation.
For each distinct prime, multiply the highest exponent power that appears.
Multiply each numerator and denominator to convert to the shared LCD.
Break down each denominator into prime factors and take the highest power of each prime:
Example: Denominators 8 (2³) and 12 (2² × 3) → Take 2³ × 3 = 24.
List consecutive multiples of each denominator until you find the first common value:
Ideal for small denominators and quick mental arithmetic.
Prime factors: 4 = 2², 10 = 2 × 5, 15 = 3 × 5. Highest powers: 2² × 3 × 5:
With LCD = 24, scale 1/6 by (4/4) and scale 3/8 by (3/3):
Multiplying all denominators together (e.g. 6 × 8 × 12 = 576) produces massive numerators that require painful reduction later. Finding the LCD (24) keeps arithmetic small and simple.
Decomposes every denominator into prime power factors (e.g. 12 = 2² × 3) and extracts the maximum power of each prime algorithmically.
Rewrites each fraction side by side with its exact multiplier (e.g., 1/6 × 4/4 = 4/24), preparing expressions for instant addition or subtraction.
Finding the LCM of 4 or 5 denominators manually is notoriously error-prone. This tool computes multi-term LCMs instantly in your browser.
Dynamically add and delete fractions with instant real-time LCD recalculation on every keystroke.
Displays prime factorizations for all denominators and highlights the highest exponent collected for each prime.
Provides scaled equivalent fractions and division verification checks confirming divisibility.
Prime factorize denominators: 6 = 2 × 3, and 8 = 23. Pick highest power of each prime: 23 × 3 = 8 × 3 = 24:
Denominators 4 (22), 5 (5), 6 (2 × 3). Combine highest prime powers: 22 × 3 × 5 = 60:
| Denominator Pair | Greatest Common Divisor (GCD) | Least Common Denominator (LCD) | Simple Product (D1 × D2) |
|---|---|---|---|
| 4 and 6 | 2 | 12 | 24 |
| 6 and 8 | 2 | 24 | 48 |
| 6 and 9 | 3 | 18 | 54 |
| 8 and 12 | 4 | 24 | 96 |
| 10 and 15 | 5 | 30 | 150 |
Do not just multiply denominators together. While multiplying gives a valid common denominator, finding the true LCD keeps numbers substantially smaller, saving you from having to reduce enormous numbers at the end of the problem.
When adding measurements like 3/8 in and 5/16 in, the LCD is simply 16 because 8 divides evenly into 16. In imperial trade work, the LCD is almost always the largest power of 2 among your denominators (16, 32, or 64).
Add fractions with like or unlike denominators and LCD steps.
Order multiple fractions ascending or descending with LCD.
Reduce fractions to simplest form using Euclidean GCD.
Generate and test equivalent proportional fractions.
All-in-one arithmetic operations for fractions and mixed numbers.
Compare fractions using butterfly cross-multiplication.
