Common Denominator Calculator
Find the least common denominator (LCD) of fractions with step-by-step solutions
Enter Your Fractions
Common Denominator Results
Equivalent Fractions with Common Denominator
Step-by-Step Solution
Example Calculations
Example 1: Two Fractions
Find LCD of: 1/3 and 2/7
Denominators: 3 and 7
Prime factors: 3 = 3¹, 7 = 7¹
LCM: 3¹ × 7¹ = 21
Equivalent fractions: 7/21 and 6/21
Example 2: Three Fractions
Find LCD of: 3/4, 4/5, and 2/3
Denominators: 4, 5, and 3
Prime factors: 4 = 2², 5 = 5¹, 3 = 3¹
LCM: 2² × 3¹ × 5¹ = 60
Equivalent fractions: 45/60, 48/60, and 40/60
Methods to Find LCD
List Multiples
List multiples of each denominator
Find first common multiple
Prime Factorization
Break down into prime factors
Use highest powers of each prime
Using GCF
LCM = (a × b) / GCF(a,b)
For two numbers only
Key Concepts
LCD = LCM of all denominators
LCD is the smallest common denominator
Infinite common denominators exist
Used for adding/subtracting fractions
Prime factorization is most reliable
Understanding Common Denominators
What is a Common Denominator?
A common denominator is a number that is a multiple of all denominators in a set of fractions. The least common denominator (LCD) is the smallest positive number that all denominators can divide into evenly.
Why Find the LCD?
- •Add and subtract fractions with different denominators
- •Compare fractions easily
- •Create equivalent fractions
- •Simplify complex fraction operations
Prime Factorization Method
Step 1: Find prime factors of each denominator
Step 2: Identify highest power of each prime
Step 3: Multiply all highest powers together
Example Process
Find LCD of 12 and 18:
12 = 2² × 3¹
18 = 2¹ × 3²
Highest powers: 2², 3²
LCD = 2² × 3² = 36