Lowest Common Denominator Calculator
Find the LCD of up to 5 fractions with step-by-step solutions
Calculate Lowest Common Denominator
1st Fraction
2nd Fraction
Results
Equivalent Fractions:
Example Calculations
Example 1: Simple Fractions
Problem: Find LCD of 2/3 and 7/4
Denominators: 3, 4
LCM(3, 4): 12
Result: 2/3 = 8/12, 7/4 = 21/12
Example 2: Three Fractions
Problem: Find LCD of 1/4, 1/6, and 1/8
Denominators: 4, 6, 8
LCM(4, 6, 8): 24
Result: 1/4 = 6/24, 1/6 = 4/24, 1/8 = 3/24
Example 3: Mixed Numbers
Problem: Find LCD of 1 1/2 and 2 1/3
Convert to improper: 3/2 and 7/3
Denominators: 2, 3
LCM(2, 3): 6
Result: 3/2 = 9/6, 7/3 = 14/6
LCD Formulas
LCM of Two Numbers
LCM(a,b) = |a × b| / GCD(a,b)
Mixed to Improper
W n/d = (W×d + n)/d
Equivalent Fraction
a/b = (a×k)/(b×k)
Quick Tips
LCD is the smallest positive integer that all denominators divide into
LCD is essential for adding and subtracting fractions
For comparing fractions, convert to same denominator using LCD
LCD = LCM of all denominators
Understanding Lowest Common Denominator
What is LCD?
The Lowest Common Denominator (LCD) is the smallest positive integer that serves as a common denominator for a set of fractions. It's equivalent to the Least Common Multiple (LCM) of the denominators.
Why is LCD Important?
- •Essential for adding and subtracting fractions
- •Allows comparison of fractions
- •Simplifies fraction operations
- •Used in solving algebraic equations with fractions
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 multiply highest powers
Method 3: GCD Formula
Use LCM(a,b) = (a × b) / GCD(a,b)
Real-World Applications
Cooking & Recipes
When combining ingredients with different fractional measurements, LCD helps convert them to a common unit for easier calculation.
Music & Time Signatures
Musicians use LCD to combine different note values and rhythms when working with complex time signatures.
Engineering & Construction
Converting between different measurement systems and calculating material quantities often requires finding common denominators.
Financial Calculations
When dealing with different fractional interest rates or payment schedules, LCD helps standardize calculations.