# mid-aughts

Jim Parish jparish at SIUE.EDU
Thu Mar 15 15:46:57 UTC 2007

```Arnold M. Zwicky wrote:
> the relevant mathematical concepts are named "least common multiple"
> and "greatest common denominator/divisor".

Eek! As a professional mathematician, I can't let this go. "Greatest
common divisor", yes; "greatest common denominator", no. It's "least
common denominator" - which is the least common multiple of the
denominators of two fractions which are being added. There isn't any
*greatest* common denominator, since any common denominator could
be, e.g., multiplied by two to get another, greater, common
denominator. To put it another way: the set of common divisors of two
integers is bounded above, and the greatest of them is of interest; the
set of common denominators of two fractions is bounded below, and the
least of them is the one desired.

Jim Parish

------------------------------------------------------------
The American Dialect Society - http://www.americandialect.org

```