# lowest common denominator

James A. Landau JJJRLandau at AOL.COM
Tue Aug 14 21:31:56 UTC 2001

```In a message dated 08/14/2001 5:02:21 PM Eastern Daylight Time,
savan at EROLS.COM writes:

> Does anyone know the origins of "lowest common denominator"? Of course
>  it's from math, but when and how did it acquire its current meaning?

For the mathematical meaning, Jeff Miller's "Earliest Known Uses of Some of
the Words of Mathematics" page

URL http://members.aol.com/jeff570/mathword.html

gives the following:

<quote, with some editing>

"Common denominator" appears in English in 1594 in Exercises by Blundevil:
"Multiply the Denominators the one into the other, and the Product thereof
shall bee a common Denominator to both fractions" (OED2).

"Common divisor" was used in 1674 by Samuel Jeake in Arithmetick, published
in 1696: "Commensurable, called also Symmetral, is when the given Numbers
have a Common Divisor" (OED2).

"Least common multiple" is dated 1823 in MWCD10 (Webster 10th Collegiate).

"Least common denominator" is found in 1851 in _Arithmetic, designed for
academies and schools_ by Charles Davies: "It is often necessary to reduce
fractions to their least common denominator"

"Least common dividend" appears in 1857 in _Mathematical Dictionary and
Cyclopedia of Mathematical Science_.

The terms "lowest common denominator" and "lowest common multiple"
(abbreviated L. C. M.) appear in 1881 in _Elements of Algebra_ by G. A.
Wentworth.

<end quote>

The popular meaning of the term just about reverses the mathematical meaning.
The "least common multiple" is GREATER than the numbers it is common to.
The popular meaning is closer to the mathematical "greatest common factor".

Presumably some non-mathematician, needing a catchy phrase for "that small
part understandable or usable by all" thought of the word "lowest" or "least"
and was led by an incorrect memory of arithmetic to jump to "least common
denominator".

I say "catchy phrase" because "least common denominator" in popular usage is
usually a polemical term, and my guess (it is only a guess) is that the term
was first popularized by someone writing a polemic about watered-down
American education or some such.

- Jim Landau  (who can be very snobbish towards non-mathematicians)

```