Least Common Denominator in Math: Definition & Examples

Definitionnoun phrase

What is the least common denominator?

The least common denominator (LCD) of two or more fractions is the smallest number that every denominator divides into evenly. It is the least common multiple of the denominators. For 14 and 56, the LCD is 12, so you rewrite them as 312 and 1012 before you add, subtract or compare.

In Spanish: mínimo común denominador
Also called: LCD, lowest common denominator
Grade level: K-5

Grade 5Grade 6Grade 7CCSS 5.NF.A.1CCSS 6.NS.B.4GEDASVABTABEHiSETACCUPLACER

Least Common Denominator in a picture

12 is the first number on both lists, so it is the least common denominator. 24 also works, but it makes bigger numbers to simplify later.

Formal definition and notation

The LCD of fractions ab and cd is LCM(b, d), the least common multiple of their denominators. Each fraction is then rewritten as an equivalent fraction with that denominator by multiplying its numerator and denominator by the same whole number. Any common multiple of the denominators works as a common denominator, but the least one keeps the numbers smallest. If the denominators share no factor except 1, the LCD is their product; if one denominator divides the other, the LCD is the larger one.

Symbol	Read it as	Meaning
LCD	L C D, least common denominator	the smallest shared denominator for a group of fractions
LCM(4, 6) = 12	the least common multiple of 4 and 6 is 12	the same number as the LCD of fractions with denominators 4 and 6

Key facts

Listing method: write multiples of the largest denominator until you reach one the others divide. For 4 and 6: 6 no, 12 yes.
Prime factor method: 8 = 2³ and 12 = 2² × 3, so the LCD uses 2³ × 3 = 24.
No shared factors: the LCD of 15 and 27 is 5 × 7 = 35.
One divides the other: the LCD of 13 and 512 is 12.
You need a common denominator to add, subtract or compare fractions; you do not need one to multiply or divide them.
The same idea works in algebra: the LCD of 1x and 3x² is x².

LCD formula

LCD = LCM(b, d) = b × dGCF(b, d)

b, d: the denominators of the two fractions
GCF: their greatest common factor

For 14 and 56: 4 × 62 = 12. For three fractions, find the LCM of all three denominators.

Try it: rename a fraction

Interactive

The bars show 1/4 cut into more pieces: 2/8, 3/12, and so on. Change the fraction to 5/6 and find the row with twelfths. Twelfths is the first size both fractions share, which is the LCD.

This interactive needs JavaScript. The worked examples below show the same ideas step by step.

Least Common Denominator examples, step by step

Example 1: Find the LCD

Warm-up

Find the least common denominator of 16 and 38.

Multiples of 8: 8, 16, 24, 32, …
Check each against 6: 8 no, 16 no, 24 yes.

Answer: The LCD is 24.

Example 2: Add with the LCD

Core

Add 56 + 49.

The LCD of 6 and 9 is 18.
56 = 5 × 36 × 3 = 1518 and 49 = 4 × 29 × 2 = 818.
Add the numerators: 1518 + 818 = 2318.
As a mixed number, 2318 = 1518.

Answer: 56 + 49 = 2318 = 1518.

Example 3: Order three fractions

Test-style

Put 23, 34 and 58 in order from least to greatest.

The LCD of 3, 4 and 8 is 24.
23 = 1624, 34 = 1824, 58 = 1524.
With the same denominator, compare numerators: 15 < 16 < 18.

Answer: Using the LCD 24, the order is 58, 23, 34.

Common mistakes

✗ MistakeAdding denominators: 14 + 56 = 610.

✓ InsteadUse the LCD 12: 312 + 1012 = 1312.

The denominator names the size of the pieces. You can only add pieces of the same size, and adding denominators changes the size.

✗ MistakeTaking the product as the LCD: for 14 and 16, using 24.

✓ InsteadThe LCD is 12, because 12 is a multiple of both 4 and 6.

The product is always a common denominator, but it is the least one only when the denominators share no factor. 24 works, but then you must simplify.

✗ MistakeChanging only the denominator: 14 = 112.

✓ InsteadMultiply the top and bottom by 3: 14 = 312.

To keep the value the same, multiply the numerator and the denominator by the same number.

✗ MistakeUsing the greatest common factor: the LCD of 14 and 16 is 2.

✓ InsteadThe LCD is the least common multiple, 12.

The denominator must be divisible by both 4 and 6, so it has to be at least as large as each of them.

Not to be confused with

Least Common Denominatorvs.Least common multiple

The LCM is a property of whole numbers: LCM(4, 6) = 12. The LCD applies that idea to the denominators of fractions, so it is the same number used for a specific job.

Least Common Denominatorvs.Common denominator

A common denominator is any shared denominator: 12, 24 and 36 all work for 14 and 56. The least common denominator is the smallest of them, 12.

Least Common Denominatorvs.Greatest common factor

The GCF is the largest number that divides both numbers: GCF(4, 6) = 2. It is used to simplify fractions, while the LCD is used to add and compare them.

Quick check: 3 questions

Question 1 of 3

What is the LCD of 310 and 715?

Show answer and explanation

Answer: C. Multiples of 15: 15, 30. 30 is also a multiple of 10, so the LCD is 30. 150 is the product, which works but is not least; 5 is the GCF; 60 is a common multiple but not the least.

Question 2 of 3

The LCD of 29 and 16 is 18. How is 29 written with that denominator?

Show answer and explanation

Answer: A. 18 ÷ 9 = 2, so multiply the top and bottom by 2: 418. 218 changes only the denominator, 1118 adds 9 to the numerator, and 318 is 16 renamed.

Question 3 of 3

What is 18 + 512?

Show answer and explanation

Answer: B. With the LCD 24: 324 + 1024 = 1324. 620 adds tops and bottoms, 624 forgets to rename the numerators, and 1348 renames the numerators for 24 but writes 48.

Least Common Denominator: frequently asked questions

How do you find the least common denominator?

List the multiples of the largest denominator and stop at the first one that every other denominator divides. For 6 and 8: 8, 16, 24, and 24 is divisible by 6, so the LCD is 24. For larger numbers, use prime factorization: take each prime the greatest number of times it appears in any one denominator, then multiply.

Is the LCD the same as the LCM?

They are the same number, used in different settings. The least common multiple is defined for any whole numbers, such as LCM(6, 8) = 24. The least common denominator is the LCM of the denominators of fractions, so the LCD of 1/6 and 3/8 is 24. When people say LCD, they are always talking about fractions.

Do you have to use the least common denominator?

No. Any common denominator gives the right answer, as long as you rename both fractions correctly. Using a larger one, such as the product of the denominators, just makes bigger numbers: 14 + 16 = 624 + 424 = 1024, which you then simplify to 512. The LCD gives 512 directly.

Practice and tools

Least Common Denominator CalculatorFind the LCD of several fractions Adding Fractions with Unlike Denominators CalculatorAdd fractions step by step with the LCD GCF and LCM CalculatorFind the LCM of the denominators

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 5.NF.A.1, CCSS 6.NS.B.4

Cite this entry

Effortless Math Team. “Least Common Denominator.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/least-common-denominator/

Flashcard

TermLeast Common DenominatorLCD

DefinitionThe smallest denominator two fractions can share; the LCM of the denominators. 14 and 56: LCD 12, so 312 and 1012.

Study the full deck

Browse all terms in the Math Dictionary · More number system terms · Random term

Least Common MultipleThe least common multiple (LCM) is the smallest positive multiple shared by two or more numbers. The LCM of 6 and 9 is 18: it is the first number on both lists of multiples, 6, 12, 18, … and 9, 18, …. The LCM of the denominators is the least common denominator for adding fractions.Number System · Grade 5, Grade 6, Grade 7DenominatorThe denominator is the bottom number in a fraction. It tells how many equal parts make one whole: in 35, the 5 means the whole is cut into 5 equal parts, and the numerator 3 counts the parts you have. The denominator can never be 0.Number System · Grade 3, Grade 4, Grade 5Equivalent FractionsEquivalent fractions are fractions that name the same value, like 12, 24 and 36. To make one, multiply or divide the numerator and denominator by the same nonzero number. That multiplies the fraction by 1, so its value does not change, and the fractions land on the same point of a number line.Number System · Grade 3, Grade 4, Grade 5NumeratorThe numerator is the top number in a fraction. It tells how many parts are being counted, while the denominator below the fraction bar tells how many equal parts make one whole. In 35, the numerator is 3: three of five equal parts are taken.Number System · Grade 3, Grade 4, Grade 5Whole NumberA whole number is 0 or a positive counting number: 0, 1, 2, 3, and so on. Whole numbers do not include fractions, decimals, or negative numbers, so 12 is a whole number but 8.5, 34 and −3 are not. Every whole number is also an integer.Number System · Grade 3, Grade 4, Grade 5Common DenominatorA common denominator is a number that can be used as the denominator of two or more fractions at once. It is any common multiple of the denominators. For 13 and 14, 12 works: 412 and 312. You need one to add, subtract or compare fractions with different denominators.Number System · Grade 4, Grade 5, Grade 6NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Greatest Common FactorThe greatest common factor (GCF) is the largest factor shared by two or more numbers: the largest number that divides into both without a remainder. The GCF of 18 and 24 is 6. Find it by listing factors or by multiplying the prime factors the numbers share. The GCF is how you simplify fractions in one step.Number System · Grade 5, Grade 6, Grade 7Mixed NumberA mixed number has a whole number and a fraction together, such as 234, which means 2 + 34. It represents a value greater than one whole when the whole-number part is positive. Every mixed number can be rewritten as an improper fraction, and back: 234 = 114.Number System · Grade 4, Grade 5, Grade 6SimplifySimplify means to rewrite a number or expression in a shorter, easier form without changing its value. To simplify a fraction, divide the numerator and denominator by a common factor until none is left: 1824 = 34. To simplify an expression, combine like terms and do the operations you can: 3x + 2x = 5x.Number System · Grade 4, Grade 5, Grade 6Prime FactorizationPrime factorization is writing a whole number as a product of prime numbers only, such as 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3². Find it with a factor tree or repeated division. Every whole number greater than 1 has exactly one prime factorization, apart from the order of the factors.Number System · Grade 4, Grade 5, Grade 6MultipleA multiple of a number is the result of multiplying that number by any whole number. The multiples of 4 are 4, 8, 12, 16, and so on, continuing without end. Every number is a multiple of itself and of 1. To test a number, divide: if the remainder is 0, it is a multiple.Number System · Grade 4, Grade 5, Grade 6Improper FractionAn improper fraction has a numerator that is greater than or equal to its denominator, so its value is 1 or more. Examples are 74, 92 and 55. Every improper fraction can be rewritten as a whole number or a mixed number: 74 = 134. Improper does not mean wrong.Number System · Grade 4, Grade 5, Grade 6Simplest FormSimplest form is the way of writing a fraction so its numerator and denominator have no common factor other than 1. To get there, divide the top and bottom by their greatest common factor: 68 = 6 ÷ 28 ÷ 2 = 34. The value stays the same; only the numbers get smaller. It is also called lowest terms.Number System · Grade 4, Grade 5, Grade 6

Least Common Denominator

What is the least common denominator?

Least Common Denominator in a picture

Formal definition and notation

Key facts

LCD formula

Try it: rename a fraction

Least Common Denominator examples, step by step

Example 1: Find the LCD

Example 2: Add with the LCD

Example 3: Order three fractions

Common mistakes

Not to be confused with

Quick check: 3 questions

Least Common Denominator: frequently asked questions

How do you find the least common denominator?

Is the LCD the same as the LCM?

Do you have to use the least common denominator?

Related terms

Practice and tools

Sources

Flashcard

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