Common Denominator Calculator

Q: How do you find the least common denominator?

Find the least common multiple of the denominators. Write each denominator as prime factors and multiply the highest power of every prime that appears. For 4 = 2² and 6 = 2 × 3, the LCD is 2² × 3 = 12.

Q: What is the difference between LCD and LCM?

The LCD is the LCM of the denominators. LCM is the general idea for any whole numbers; LCD is the name used when those numbers are the denominators of fractions.

Q: Can I just multiply the denominators?

Multiplying the denominators always gives a common denominator, but not always the least one. For 1/4 and 1/6, 4 × 6 = 24 works, but 12 is smaller and keeps the numbers easier.

Q: How do I make equivalent fractions with the LCD?

Divide the LCD by each denominator and multiply the numerator and denominator by the result. With LCD 24, 5/6 needs × 4, so 5/6 = 20/24.

Q: How do I order fractions from least to greatest?

Rewrite them over a common denominator and compare the numerators. The calculator does this for you and shows the order with < and = signs.

Q: What is the LCD of 3, 4 and 5?

The three numbers share no prime factors, so the LCD is 3 × 4 × 5 = 60.

Enter two or more fractions to find their least common denominator. You get the equivalent fractions over the LCD, the fractions in order from least to greatest, and the prime factor working.

Least common denominator
Equivalent fractions
Order and compare
Up to 10 fractions

Fractions to compare

Find the least common denominator (LCD) of 2 to 10 fractions, rewrite them as equivalent fractions and put them in order.

LCD = 24

1 over 4=6 over 24
5 over 6=20 over 24
3 over 8=9 over 24

From least to greatest

Step-by-step working

Find the least common denominator (LCD)
4 = 2²
6 = 2 × 3
8 = 2³
LCD = 2³ × 3 = 24
The LCD is the smallest number every denominator divides into. Take each prime factor the most times it appears in any one denominator.
Rewrite each fraction with denominator 24
1 over 4=1 × 6 over 4 × 6=6 over 24
5 over 6=5 × 4 over 6 × 4=20 over 24
3 over 8=3 × 3 over 8 × 3=9 over 24
Multiply the top and the bottom by the same number, so each fraction keeps its value.
Order them from least to greatest
6 over 24<9 over 24<20 over 24
1 over 4<3 over 8<5 over 6
With the same denominator, the fraction with the bigger numerator is bigger.

Exact arithmetic for numbers of any size, with no rounding errors. Everything runs in your browser, and nothing you type leaves this page.

What is a common denominator?

A common denominator is a number that every denominator in a set of fractions divides into. The least common denominator (LCD) is the smallest one, and it is the least common multiple (LCM) of the denominators. You need a common denominator to add, subtract or compare fractions, because only then are the parts the same size. For 1/4, 5/6 and 3/8 the LCD is 24, so they become 6/24, 20/24 and 9/24, and you can see at once that 1/4 < 3/8 < 5/6. This calculator finds the LCD from the prime factors of each denominator, rewrites every fraction, and sorts them.

How to find a common denominator with this calculator

Type each fraction into the stacked boxes. Mixed numbers and whole numbers work too.
Press “Add a fraction” for up to 10 fractions.
Read the LCD, the equivalent fraction for each input and the order from least to greatest.
Check the working: each denominator is broken into prime factors, and the LCD takes every factor the most times it appears.

Common denominator rules

LCD = LCM of the denominators: LCD(4, 6) = 12.
LCM(a, b) = a × b ÷ GCF(a, b): LCM(4, 6) = 24 ÷ 2 = 12.
a/b = (a × k)/(b × k), k = LCD ÷ b: 5/6 with LCD 24: k = 4, so 20/24.
Compare over the LCD: Bigger numerator means bigger fraction: 9/24 < 20/24.

Why use this common denominator calculator

Every step, freeThe full working is always on the page: common denominator, rewritten fractions, greatest common factor and the final simplification. No account, no premium tier and no daily limit.
Exact answers at any sizeFractions are stored as exact whole numbers, so a 40-digit numerator stays exact. There is no floating-point rounding of the kind that turns 0.1 + 0.2 into 0.30000000000000004.
Repeating decimals shown properly1/7 is shown as 0.142857 with a bar over the repeating block, instead of being cut off at 0.1428571429. You also get a rounded value to copy.
Fast and privateThe answer updates as you type and is worked out on your device. Nothing you enter is sent to a server, and the calculator keeps working if your connection drops.

How it compares with other fraction calculators

Feature	This calculator	Typical online calculators
More than two numbers in one problem	Yes, up to 10, with order of operations	Usually two
Fractions, mixed numbers, whole numbers and decimals together	Yes	Often separate calculators
Full step-by-step working	Always free	Often missing or behind a paywall
Repeating decimals	Exact, with a bar over the repeating digits	Rounded to a few places
Very large numbers	Exact at any size	Rounded or a separate big number tool
Decimal to fraction for repeating decimals	Type 0.1(6) or 0.1666...	Count the repeating digits yourself
Privacy	Runs in your browser, nothing sent	Inputs often sent to a server

Common uses

Adding fractions by hand. Get the LCD and the rewritten fractions before you add.
Comparing fractions. Is 5/8 bigger than 3/5? Put them over 40 and look at the numerators.
Worksheets. Check equivalent fractions and ordering exercises quickly.
Algebra. Find the LCD of number denominators before combining rational terms.

More math help: the percentage calculator for percent questions, the ratio calculator for simplifying and scaling ratios, and the math editor to type up your working as a neat equation.

Fraction words explained

Numerator: The top number. It counts how many parts you have.
Denominator: The bottom number. It says how many equal parts make one whole.
Proper fraction: The numerator is smaller than the denominator, such as 3/4.
Improper fraction: The numerator is as big as or bigger than the denominator, such as 7/4.
Mixed number: A whole number and a proper fraction together, such as 1 3/4.
Equivalent fractions: Different fractions with the same value, such as 1/2, 2/4 and 50/100.
Least common denominator: The smallest number all the denominators divide into.
Greatest common factor: The biggest number that divides both the numerator and the denominator.
Reciprocal: A fraction turned upside down. The reciprocal of 2/3 is 3/2.
Repeating decimal: A decimal whose digits repeat forever, such as 0.333... for 1/3.

For example, in 3 over 4 the numerator is 3 and the denominator is 4.

Worked example: 1/4, 5/6 and 3/8

Break the denominators into primes: 4 = 2², 6 = 2 × 3 and 8 = 2³. Take the highest power of each prime: 2³ and 3, so the LCD is 8 × 3 = 24. Rewrite each fraction: 1/4 = 6/24 (× 6), 5/6 = 20/24 (× 4) and 3/8 = 9/24 (× 3). Comparing the numerators gives the order 6/24 < 9/24 < 20/24, so 1/4 < 3/8 < 5/6.

What to expect from the result

The LCD is calculated exactly for denominators of any size. Prime factors are shown for denominators up to 10 billion; larger ones are combined with the LCM formula instead. Fractions are rewritten as you entered them, so 2/4 and 1/2 both count, and equal fractions are marked with =.