Least common denominator at a glance
The LCD is the LCM of the written denominators. It works for several fractions, creates equivalent forms, and can be explained step by step.
Exact, visual, step by step
Least Common Denominator Calculator
Find the least common denominator of two or more fractions, convert them to equivalent fractions, and compare LCM, prime factorization, and multiples methods.
LCD(a/b, c/d) = LCM(|b|, |d|)
How the Least Common Denominator Calculator Works
Enter fractions, read and normalize their denominators, calculate the LCM, and scale every numerator by LCD divided by its denominator.
How to Calculate the Least Common Denominator
Prime factorization keeps the highest exponent of each prime. The multiples method finds the first shared positive multiple.
Least Common Denominator Formula
For several fractions, the LCD is the least common multiple of the absolute denominator values.
LCD = LCM(|d₁|, |d₂|, …, |dₙ|)
Worked example: three fourths and five sixths
Four equals two squared and six equals two times three. Their LCD is twelve, so the equivalent fractions are nine twelfths and ten twelfths.
LCD versus LCM
LCM applies to integers generally. LCD is the LCM used specifically for fraction denominators.
LCD versus GCF
LCD finds the smallest shared multiple, while GCF finds the largest shared factor.
Common denominator versus LCD
Any positive multiple of the LCD is a common denominator, but only the smallest one is the LCD.
How the LCD Creates Equivalent Fractions
Multiply the numerator and denominator by the same scale factor to preserve the fraction value.
Using the LCD to Add Fractions
Convert unlike fractions to the LCD, add their numerators, and simplify the result.
Using the LCD to Subtract Fractions
Convert to a shared denominator, subtract the numerators in order, and simplify.
Common LCD Examples
| 2, 3 → 6 |
| 3, 4 → 12 |
| 4, 6 → 12 |
| 6, 8 → 24 |
| 12, 18 → 36 |
Common Least Common Denominator Mistakes
Do not use numerators, allow denominator zero, change only a denominator, confuse GCF with LCM, or multiply denominators without checking for a smaller LCM.
Least Common Denominator Tools
Choose a specialized calculator for a particular number of fractions, operation, method, or fraction type.
fraction-bars
LCD of Two Fractions
Find and align exactly two fractions.
→fraction-barsLCD of Three Fractions
Find one denominator shared by exactly three fractions.
→flowLCD of Multiple Fractions
Add or remove fractions in a dynamic list.
→multiplesCommon Denominator Calculator
Find the LCD and additional common denominators.
→proportionEquivalent Fractions Calculator
Scale one fraction to a valid target denominator.
→before-afterFractions to Common Denominator
Rewrite several fractions over their LCD.
→merge-barsAdd Fractions with Different Denominators
Convert, add, and simplify unlike fractions.
→remove-barSubtract Fractions with Different Denominators
Convert, subtract, and simplify unlike fractions.
→number-lineCompare Fractions
Compare two fractions using exact common forms.
→number-lineOrder Fractions
Sort several fractions in ascending or descending order.
→prime-factorsLCD Using Prime Factorization
Select the largest exponent of every prime factor.
→multiplesLCD Using Multiples
Find the first intersection in lists of multiples.
→factor-mapLCD Using GCF
Use the GCD and product relationship.
→flowLCM of Denominators
Calculate the LCM of denominator integers.
→whole-barsMixed Number Common Denominator
Align the fractional parts of mixed numbers.
→whole-barsImproper Fraction LCD
Preserve improper fractions while finding their LCD.
→signed-lineNegative Fractions LCD
Normalize signs and return a positive LCD.
→whole-barsWhole Number and Fraction
Treat the whole number as having denominator one.
→sequenceFraction Addition Step by Step
Learn all six addition stages.
→sequenceFraction Subtraction Step by Step
Learn all six subtraction stages.
→factor-cancelSimplify After Common Denominator
Reduce a result using its GCD.
→scaling-arrowTarget Common Denominator
Check and create a requested denominator.
→method-switcherLCD Step by Step Solver
Switch among LCM, prime factorization, and multiples.
→Related Learning Guides
Learn the LCD methods, the relationship among LCD, LCM, and GCF, and how unlike fractions are added.
GuidesLeast Common Denominator Questions
What is a least common denominator?
It is the smallest positive number divisible by every written denominator.
Is LCD the same as LCM?
The operation is the same, but LCD refers specifically to fraction denominators.
How do you find the LCD of three fractions?
Calculate the LCM of all three denominators and scale each numerator.
Can a common denominator be larger than the LCD?
Yes. Every positive multiple of the LCD is also a common denominator.
What if the denominators already match?
Their shared denominator is already the LCD.