Lowest common denominator
lowest common multiple of the denominators of a set of fractions
In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions.
Description
The lowest common denominator of a set of fractions is the lowest number that is a multiple of all the denominators: their lowest common multiple.
The product of the denominators is always a common denominator, as in:
1
2
+
2
3
=
3
6
+
4
6
=
7
6
{\displaystyle {\frac {1}{2}}+{\frac {2}{3}}\;=\;{\frac {3}{6}}+{\frac {4}{6}}\;=\;{\frac {7}{6}}}
but it is not always the lowest common denominator, as in:
5
12
+
11
18
=
15
36
+
22
36
=
37
36
{\displaystyle {\frac {5}{12}}+{\frac {11}{18}}\;=\;{\frac {15}{36}}+{\frac {22}{36}}\;=\;{\frac {37}{36}}}
Here, 36 is the least common multiple of 12 and 18. Their product, 216, is also a common denominator, but calculating with that denominator involves larger numbers:
5
12
+
11
18
=
90
216
+
132
216
=
222
216
.
{\displaystyle {\frac {5}{12}}+{\frac {11}{18}}={\frac {90}{216}}+{\frac {132}{216}}={\frac {222}{216}}.}
With variables rather than numbers, the same principles apply:
a
b
c
+
c
b
2
d
=
a
b
d
b
2
c
d
+
c
2
b
2
c
d
=
a
b
d
+
c
2
b
2
c
d
{\displaystyle {\frac {a}{bc}}+{\frac {c}{b^{2}d}}\;=\;{\frac {abd}{b^{2}cd}}+{\frac {c^{2}}{b^{2}cd}}\;=\;{\frac {abd+c^{2}}{b^{2}cd}}}
Some methods of calculating the LCD are at Least common multiple § Calculation.
Role in arithmetic and algebra
The same fraction can be expressed in many different forms. As long as the ratio between numerator and denominator is the same, the fractions represent the same number. For example:
2
3
=
6
9
=
12
18
=
144
216
=
200
,
000
300
,
000
{\displaystyle {\frac {2}{3}}={\frac {6}{9}}={\frac {12}{18}}={\frac {144}{216}}={\frac {200,000}{300,000}}}
because they are all multiplied by 1 written as a fraction:
2
3
=
2
3
×
3
3
=
2
3
×
6
6
=
2
3
×
72
72
=
2
3
×
100
,
000
100
,
000
.
{\displaystyle {\frac {2}{3}}={\frac {2}{3}}\times {\frac {3}{3}}={\frac {2}{3}}\times {\frac {6}{6}}={\frac {2}{3}}\times {\frac {72}{72}}={\frac {2}{3}}\times {\frac {100,000}{100,000}}.}
It is usually easiest to add, subtract, or compare fractions when each is expressed with the same denominator, called a "common denominator".
Begin with the source’s own compact description: “Lowest common denominator” is lowest common multiple of the denominators of a set of fractions. The dossier treats that line as a proposition to test through Lowest, common and denominator, not as a finished interpretation.
Why this record matters
The phrase “lowest common multiple of the denominators of a set of fractions” supplies a clear boundary for inquiry. It also exposes the unanswered questions: who defined that boundary, when it became stable and which sources sit outside it.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Apr 23, 2026. The linked authority identifier is Q2144533. None of the 0 selected statements returned an explicit reference.
A concise general-reference account can conceal disagreements about scope, terminology or the weight assigned to individual sources. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Lowest common denominator”, its source revision and the description used here.
- Expand the search: follow Lowest common denominator primary sources, Lowest common denominator archive and Lowest research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Lowest common denominator”?
- Which institution is responsible for the underlying evidence?
- Which cited source is closest to the event, object or claim?
Search terms from this dossier
This entry incorporates text from “Lowest common denominator” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.