Find the least common denominator of two or more fractions so they can be added, subtracted, or compared on equal terms.
Share this calculator
Also in Fractions
Fraction Fundamentals
A least common denominator calculator finds the smallest denominator that two or more fractions can share, which is the first step when adding, subtracting, or comparing fractions with unlike denominators.
The least common denominator is the least common multiple of the denominators of two or more fractions. It is the smallest number that each denominator divides into evenly, allowing the fractions to be rewritten with matching denominators.
Using the LCD rather than any common denominator keeps the numbers small, which simplifies arithmetic and reduces the need for heavy simplification at the end.
List the multiples of each denominator until a shared multiple appears, or use prime factorisation to build the LCD from the highest powers of all prime factors present. For two denominators, the formula LCD = (b × d) / GCF(b, d) is often the fastest approach.
LCD(b, d) = (b × d) / GCF(b, d)
The least common denominator equals the product of the two denominators divided by their greatest common factor.
Once the LCD is found, multiply each fraction's numerator and denominator by the factor needed to reach the LCD. The fractions are now equivalent but share the same denominator, so they can be added, subtracted, or compared directly.
Frequently asked questions
The LCD is the LCM of the denominators specifically. The term LCD is used in the context of fractions, while LCM applies to any set of integers.
That gives a valid common denominator but not necessarily the least one. Using the LCD keeps numbers smaller and reduces simplification work.
Yes. Find the LCM of all the denominators at once by taking the highest power of each prime factor that appears in any denominator.
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
Find the least common multiple or greatest common divisor of two whole numbers with step-by-step working.
Add two or more fractions with like or unlike denominators, find the common denominator automatically, and simplify the result.
Compare two fractions side by side, convert to common denominators or decimals, and see which fraction is larger or if they are equal.
Subtract fractions with like or unlike denominators, find the common denominator automatically, and simplify the result.
