What is a common denominator?
A common denominator of two or more fractions is a number that is divisible by each of their denominators. To give fractions a common denominator, both the numerator and denominator of each fraction are multiplied by the appropriate factor.
The least common denominator (LCD) is the least common multiple (LCM) of all the denominators. That is what this calculator finds.
How to find the common denominator
- Reduce each fraction to lowest terms (if possible).
- Find the LCM of all denominators — this is the least common denominator.
- For each fraction, find its scaling factor: LCD ÷ denominator.
- Multiply the numerator and denominator of each fraction by its scaling factor.
Example 1. Common denominator of 1/4 and 1/6
- Both fractions are already in lowest terms
- LCM(4, 6) = 12
- Scaling factors: 12 ÷ 4 = 3 and 12 ÷ 6 = 2
- Multiply: 14 = 1 · 34 · 3 = 312 16 = 1 · 26 · 2 = 212
Common denominator: 12
Example 2. Common denominator of 2/6, 3/8, and 5/12
- Reduce: 2/6 = 1/3 (GCD = 2); the others are already in lowest terms
- LCM(3, 8, 12) = 24
- Scaling factors: 24 ÷ 3 = 8, 24 ÷ 8 = 3, 24 ÷ 12 = 2
- Multiply: 13 = 824 38 = 924 512 = 1024
Common denominator: 24