# [Python-Dev] Re: Stability and change

Steve Holden sholden@holdenweb.com
Tue, 28 May 2002 08:54:24 -0400

```    ----- Original Message -----
From: "Martin v. Loewis" <martin@v.loewis.de>
To: "François Pinard" <pinard@iro.umontreal.ca>
<python-dev@python.org>
Sent: Monday, May 27, 2002 2:21 AM
Subject: Re: [Python-Dev] Re: Stability and change

pinard@iro.umontreal.ca (François Pinard) writes:

> > I also use 2.0 as the lowest common denominator.
>
> Linguistic problem :-).  Should we say "greatest" instead of "lowest"?
> Granted that the greatest common denominator is not "greatest" in any
other
> way, but it is lower or equal than any of the things we consider.  The
real
> "lowest" common denominator might be very close to nothing, might it
not?

For any two natural numbers, the lowest common denominator is
1. Finding the greatest (largest?) common denominator is indeed what
involves an algorithm.

This terminology came from fractions. The canonical form of a fraction uses
the lowest possible number as the denominator. When performing additive
operations on fractions, the easiest way to proceed is to convert them to a
form with the same number as a denominator. The usual choice is the lowest
common denominator, which is the smallest number that can be used as the
denominator in both fractions. This is the LCM (least common multiple) of
the two denominators.

e.g.:

2/3 + 3/8
= 16/24 + 9/24 [24 being the LCD]
= 25/24
= 1 1/24

It doesn't therefore (IMO) make much sense to talk about the lowest common
denominator of any two natural numbers. The LCM, yes. The LCD, no.

It makes even less sense to talk about the lowest common denominator of
Python implementations, except in the metaphorical sense Mark (I believe)
intended.