Least Common Denominator Calculator
Find the LCD of fractions to add, subtract, or compare them easily
Calculate Least Common Denominator
1st Fraction
2nd Fraction
LCD Calculation Results
Example Calculation
Find LCD of 3/8 and 5/12
Given fractions: 3/8 and 5/12
Denominators: 8 and 12
Goal: Find LCM(8, 12)
Step-by-Step Solution
1. Prime factorization: 8 = 2³, 12 = 2² × 3
2. LCM = 2³ × 3 = 8 × 3 = 24
3. Convert fractions:
• 3/8 = (3×3)/(8×3) = 9/24
• 5/12 = (5×2)/(12×2) = 10/24
LCD = 24
Key Concepts
Least Common Denominator
The smallest positive integer that all denominators divide into
Least Common Multiple
LCD is the LCM of all denominators
Greatest Common Divisor
Used in the formula: LCM(a,b) = (a×b)/GCD(a,b)
Quick Reference
Why Find LCD?
- • Add fractions
- • Subtract fractions
- • Compare fractions
- • Order fractions
Common LCDs
1/2, 1/3 → LCD = 6
1/4, 1/6 → LCD = 12
1/3, 1/5 → LCD = 15
1/6, 1/8 → LCD = 24
Understanding Least Common Denominator
What is LCD?
The Least Common Denominator (LCD) is the smallest positive integer that can serve as a common denominator for a set of fractions. It's essential for adding, subtracting, and comparing fractions because these operations require fractions to have the same denominator.
When to Use LCD
- •Adding fractions: 1/4 + 1/6 requires LCD = 12
- •Subtracting fractions: 3/8 - 1/6 requires LCD = 24
- •Comparing fractions: Which is larger: 2/3 or 3/4?
- •Ordering fractions: Arrange 1/2, 2/5, 3/7 from least to greatest
How to Find LCD
Method 1: List Multiples
List multiples of each denominator and find the smallest common one
Method 2: Prime Factorization
Find prime factors and take the highest power of each prime
Method 3: LCM Formula
LCM(a,b) = (a × b) / GCD(a,b)
Remember: LCD = LCM of all denominators. The LCD is always greater than or equal to the largest denominator in your set of fractions.
Practical Applications
Cooking & Recipes
Adding ingredient measurements like 1/3 cup + 1/4 cup
Construction
Combining measurements: 2 1/4 inches + 3 3/8 inches
Finance
Comparing interest rates or fractional percentages