Lowest Common Denominator

I was just thinking of the phrase “lowest common denominator” in the sense of something lowbrow that appeals to the unwashed masses, rather than something refined. And it occurred to me that in math, the lowest common denominator of a group of (natural) numbers is always going to be 1. What’s more interesting is the largest common denominator: it’s more interesting to know that 12 and 20 are both divisible by 4, than that they’re both divisible by 1.

Admittedly, I didn’t learn this part of arithmetic in the US (or even in English), so it’s possible that the phrase “lowest common denominator” is commonly understood to mean 1/n. In the example above, 1/4 is < 1/1, so 1/4 could be viewed as the lowest common denominator of 12 and 20.

But another possibility is that the phrase “lowest common denominator”, as applied to marketing and popular tastes, was originally ironic: a filmmaker might want to make a movie that appeals to the largest common denominator, i.e., one that’s as highbrow as possible, while still appealing to everyone. A critic who said that a movie appealed to the lowest common denominator would be saying that the movie appealed to the public’s basest tastes and wasn’t even trying to be good.

I haven’t found an etymological reference to confirm or disprove this, but I think it’s at least possible that the phrase started out ironic, but that over time people forgot this.

Advertisements
This entry was posted in Math, Miscellaneous. Bookmark the permalink.

9 Responses to Lowest Common Denominator

  1. Troublesome Frog says:

    Arensb,

    Just curious, but where did you learn that part of arithmetic?

    I had similar thoughts about it being a strange turn of phrase, but I always just assumed that it was just ignorance of the mathematical meaning. Now that you point it out, it would have been kind of a clever ironic statement.

    Like

  2. arensb says:

    Troublesome Frog:

    Just curious, but where did you learn that part of arithmetic?

    In western Switzerland. I seem to remember the phrases “plus grand commun dénominateur (PGCD)” and “plus petit commun multiple (PPCM)” cropping up in elementary school.

    Like

  3. Troublesome Frog says:

    Totally off topic, but I was reading your ooblick recipe, and I thought of this video. If you haven’t seen it, it’s worth a watch.

    Like

  4. vlorbik says:

    “lowest common denominator” is indeedan unfortunate word choice. but notas inconsistent as you appear to believe.ideally, one would say “least common multiple”when referring to this concept; this isabbrivated, of course, as “LCM” … not by the cursed acronym “LCD”(“least common denominator”).
    the confusion arises because “GCD”denotes “greatest common divisor“.”divisor” in this context is essentiallythe opposite of “denominator”(since the denominator is chosenby considering multiples, not factors).
    you’re certainly right in pointing outthat the least common divisorof two natural numbers is 1(and that this isn’t very interesting). and the terminology is somewhat flawed.it just isn’t flawed in the way you’ve described …

    Like

  5. vlorbik says:

    god damn it.
    this looks nothing like the “preview”.
    wordpress has garbled by copy yet again.

    Like

  6. vlorbik says:

    “my” copy. ahem.
    thank you and good day.

    Like

  7. vlorbik says:

    here it is done right (maybe):

    “lowest common denominator” is indeed
    an unfortunate word choice. but not
    as inconsistent as you appear to believe.
    ideally, one would say “least common multiple”
    when referring to this concept; this is
    abbrivated, of course, as “LCM”
    not by the cursed acronym “LCD”
    “least common denominator”).

    the confusion arises because “GCD”
    denotes “greatest common divisor“.
    “divisor” in this context is essentially
    the opposite of “denominator”
    (since the denominator is chosen
    by considering multiples, not factors).

    you’re certainly right in pointing out
    that the least common divisor
    of two natural numbers is 1
    (and that this isn’t very interesting).
    and the terminology is somewhat flawed.
    it just isn’t flawed in the way you’ve described …

    Like

  8. arensb says:

    vlorbik:

    ideally, one would say “least common multiple”when referring to this concept

    I disagree: I see more of an analogy between “2 goes into X” and “this movie will appeal to moviegoer X”. But of course, it’s an analogy, so I guess we can all have our own interpretations.

    ”divisor” in this context is essentiallythe opposite of “denominator”(since the denominator is chosenby considering multiples, not factors).

    Sorry, but I don’t understand what you’re saying here.

    god damn it.
    this looks nothing like the “preview”.

    Funny, it usually works for me. Maybe the preview widget doesn’t like IE or something. <shrug>

    Like

  9. vlorbik says:

    i promise i’ll quit right after this.
    however: you’ve missed my point completely.
    forget the analogy: i’m talking about
    “least common denominator” as it’s actually
    used in mathematical discourse.

    it refers, whether you like it or not,
    to the least common multiple,
    not divisor, of the denominators in question.

    the fact that you’ve somehow become confused
    about this point illustrates my point:
    “LCD” clashes with the much more useful
    “LCM” and “GCD”; we who toil in the field
    have reason to wish it would go away.

    as to typesetting.
    the “preview” is a misfeature.
    and not only because it shows
    extra blank lines at random.
    (i tried to get around this
    by using BR tags … which
    worked in the preview but not
    in the actual type as it appeared
    in the comment itself.)
    nothing to do with choice of browser.

    the list of supported HTML,
    on the other hand, is a good thing
    (and could have saved me some trouble
    if i’d taken it seriously).

    Like

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s