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In the New Yorker’s (May 31) article under the title, “Stephen Hawking angers Trump supporters with baffling array of long words,” Andy Borowitz wrote;

“Speaking to a television interviewer in London, the theoretical physicist, Hawking called Trump “a demagogue who seems to appeal to the lowest common denominator. --- “For a so-called genius, this was an epic fail,” Trump’s campaign manager, Corey Lewandowski, said. “If Professor Hawking wants to do some damage, maybe he should try talking in English next time.”

Later in the day, Hawking attempted to clarify his remark about the presumptive Republican Presidential nominee, telling a reporter, “Trump bad man. Real bad man.”

From the context of Professor Hawking’s remark, I take “the lowest common denominator” as referring to the “social segment of low educated, unsophisticated people,” but I’m not sure.

I thought "common denominator" is a simple mathematic term. What does it mean in the context of the above quote?

Mr. Trump’s campaign manager says Professor Hawking should try to talk in English. Is this a farfetched way of using “common denominator” from math to politics?

Did Professor Hawking misuse "the common denominator"? Or does Mr. Trump's campaign manager not understand the meaning of "common denominator", which some call an "everyday-use" English phrase?

P.S.

I found the following definition of 'common denominator' in Oxford Advanced Learners English Dictionary;

2) an idea, attitude or experience that is shared by all the members of group - see also Lowest common denominator.

Readers English Japanese Dictionary at hand, published by Kenkyu-sha, a foreign language, especially English language dictionary specialist publisher in Japan, and rated as the most reliable English Japanese dictionary totally dropped the reference to this paticular meaning.

It was a learning. I told to myself that I should have made more homework on English-to-English dictonaries beforehand.

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    I think questions that may attract personal "appreciations " on political subjects should be avoided here. – user66974 Jun 1 '16 at 6:08
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    @Josh61.Since my joining EL&U , I tried to be least political, and I 'm totally the third party with political issues in America though I read them in newspapers. I'm drawn to the meanig of the phrase in question because it's the issue of English language as one of the concerned party happened to say. I'm not looking for any of politically tilted interpretation. I'm simply asking for what the objective / acurate meaning of "common denominator" is when used for non-math arena. This is a question purely on English expression. I'm not expecting political abuse and argument from this question. – Yoichi Oishi Jun 1 '16 at 7:43
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    @Josh61 I don't think this question is related with political subjects. Comments here can cause some controversy. I am flagging them for moderators' attention. – user140086 Jun 1 '16 at 8:31
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    As a side note for those who are not aware of it, Borowitz is a humorist who writes fake over-the-top news (a la The Onion, though without The Onion's distressing tendency to be dead-on predictive). – torek Jun 12 '16 at 23:29
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    @HotLicks It was probably a slip of the tongue, conflating LCM with GCD. – Lawrence Aug 8 '16 at 12:31
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The term lowest (or least) common denominator (LCD) of a set of whole numbers (i.e., non-zero integers) is the smallest whole number that each member of the set divides evenly. Mathematically, this means that the LCD includes all the factors of each member of the set, but in the vernacular, it means the smallest thing that a group of people share, an idea akin to the smallest prime factor shared between whole numbers, a concept void of mathematical utility. The attraction of the misnomer is likely the pejorative use of lowest, the sharing aspect of common, and the meaning of denominator as a namer, labeler, or classifier.

In Hawking's case, he's talking about knowledge, saying that when Trump speaks to people he's talking so that the least knowledgable (or equivalently, the most ignorant) will approve. One of those most ignorant is Trump's campaign manager, who instead of admitting that he and Trump's partisans don't understand Hawking because they're ignorant, instead claims that Hawking is unintelligible.

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    Further, the idiom has attained an intimation of baseness. Thus the implication is that not only does Trump appeal to the most simplistic impulses of his audience, he also appeals to their most sordid emotions. – Hot Licks Jun 1 '16 at 1:58
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    The pedestrian use is completely removed from anything mathematical. When you add ⁵⁄₁₂ + ⁷⁄₁₆ and get ⁴¹⁄₄₈, the least common denominator is 48 because 48 is the smallest number that has both 12 and 16 as divisors. So it’s a shared superset of the factors. The greatest common factor between 12 and 16 is 4, which is a shared subset of the factors. Somehow the populist notion has inverted the subset and superset notion here, and broken the entire metaphor. If you want what they have in common, it's the greatest common factor; if you want what has them in common, it's the least common multiple. – tchrist Jun 1 '16 at 2:32
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    @deadrat The lowest common denominator is not “the smallest factor that two integers share”. See my extended comment for why the smallest factor that two integers share would be the least common factor, not the least common denominator as you have indicated. The least common denominator is a superset not a subset: it's the smallest superset of factors. We're logically looking for a small common subset that two things share, not for a greater superset that shares both of them in common. You do have common parlance right, but common parlance is mathematically unsound in this, an error. – tchrist Jun 1 '16 at 5:08
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    @Hot Licks. Funny. We were taught '最大公約数,' literally translated as 'greatest common factor' in math class in junior high or high school in Japan about 70 years ago. Today we use it as in " tax reduction for the benefits of the greatest common factor of populace." – Yoichi Oishi Jun 1 '16 at 23:29
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    @HotLicks I hope I'm not attracting Comment Fairies with this comment, but (common) denominators can be multiplied to get as large as needed, hence there is no finite greatest common denominator. For what it's worth, we used to use the terms "lowest common multiple" (LCM) and "highest common factor" (HCF). – Lawrence Aug 8 '16 at 11:27
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My guess at the "try talking English" comment was that the issue was with the word demagogue ("What, you mean like Thor?").

http://www.thefreedictionary.com/demagogue

The phrase "lowest common denominator" is common enough to be understood by even Trump's team, and perhaps even the segment of the population to which it refers (even if they couldn't add two fractions to save their life).

The whole thing reminds me of one of my favourite exchanges from The Simpsons:

Homer:  "Wait - that word you keep calling me..."
Artie Ziff: "Ignoramus?"
Homer: "Yes!  It means 'stupid', doesn't it?"
Artie: "There is a difference between ignorance and stupidity."
Homer: "Not to me there isn't, you ... ignoramus!"
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The expression "lowest common denominator" has appeared in figurative (in this case, non-mathematical) contexts for quite a while—indeed for almost as long as it has been used in a mathematical sense.

Merriam-Webster's Eleventh Collegiate Dictionary (2003) offers this entry for the term:

lowest common denominator n (1854) 1 : LEAST COMMON DENOMINATOR [defined elsewhere in the dictionary as "(1851) the least common multiple of two or more denominators"] 2: something of small intellectual content designed to appeal to a lowbrow audience; also : such an audience

The American Heritage Dictionary of the English Language, fifth edition (2010) divides the figurative meaning into (a) and (b) parts:

lowest common denominator n. 1. See least common denominator. 2a. The most basic, least sophisticated level of taste, sensibility, or opinion among a group of people. b. The group having such taste, sensibility, or opinion.

The American Heritage dictionary's definitions 2a and b do a better job than the Merriam-Webster dictionary's definition 2 of framing the figurative meaning of "lowest common denominator" as an extension of the mathematical sense of the term.

The joke that Andy Borowitz is making in this fictional dispute between the physicist Stephen Hawking and sometime Trump political operative Corey Lewandowski is that Hawking's vocabulary is beyond the grasp not only of Trump's lumpen supporters but even of his advisors. In effect, Lewandowski's supposed ignorance of the terms "demagogue" and "lowest common denominator" confirms Hawking's point about Trump's targeting of the lowest common denominator as his primary constituency. Later, to be coherent to the same constituency, Hawking supposedly engages in rhetoric at the Tarzan the Ape-Man level. As torek notes in a comment beneath the posted question above, the whole thing is a satirical invention of the writer.


Merriam-Webster traces "lowest common denominator" to 1854 and "least common denominator" to 1851. It is therefore quite interesting that the earliest matches for "lowest common denominator" in an Elephind newspaper database search use the term figuratively, despite appearing within twenty years of its mathematical origin.

From an untitled brief item in the Wheeling [West Virginia] Daily Intelligencer (October 18, 1873):

The feeling between the Cincinnati Commercial and Gazette, is probably reduced to its lowest common denominator in the following paragraph in an editorial in yesterday's Commercial:

"The effusion of malice and stupidity in the Gazette about the Commercial is of no personal consequence or public interest. It is the green ooze of an ancient jealousy, and, though offensive, is innocuous."

From an untitled item, again in the Wheeling [West Virginia] Daily Intelligencer (September 5, 1874):

The political affairs of the Second Congressional District are largely under the patronage of the Morgantown Post, and we are warned not to poach on its premises by ant impertinent suggestions. This exclusiveness is an improvement on the old Virginia idea of State sovereignty. It is a reduction of that idea to its lowest common denominator. Every editor should have a little patch of his own to cultivate is the English of it.

In these two politically inflected instances, "lowest common denominator" seems to mean something like "most basic and unsophisticated manifestation."

A later instance of the expression—from "How a Florida Man Saves Money and Grows Rich" in the Indianapolis [Indiana] Journal (September 9, 1894) suggests that the phrase's familiarity in the United States during this era may be owing to its use in schoolbooks:

There lives over on the banks of the St. Lucie river, not far from here, a middle-aged North Carolinian who has succeeded in reducing the cost of living to the "lowest common denominator," as he himself expresses it, borrowing the phrase from his old "Greenleaf Arithmetic."

The usage here isn't mathematically accurate, but it does suggest the application of a half-remembered original mathematical sense to a semi-figurative use. Mathematical textbooks by Benjamin Greenleaf that discuss "common denominators" go back to at least 1843, but Greenleaf evidently did not adopt the complete phrase "least [not lowest] common denominator" until about 1857.

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Lowest Common Denominator has been a term of art in the television industry since the formation of the national broadcast networks, originally CBS, NBC, and ABC.

Because the broadcasts were national, available to anyone with receivers, the content had to appeal to the broadest audience possible.

This came to be associated with mediocre content, but response is subjective and hit network shows, those with the the broadest possible audience, are the most profitable.

You can see this is the film industry, where, among the list of highest all-time grossing films adjusted for inflation there are no R ratings, and many G ratings. Studios are said to love the lowest rating because they have the greatest potential (least restricted) audience.

The use of the term here has a mathematical meaning, counter to the common mathematical meaning, in a game theoretic context: the producers are trying to maximize their minimum audience.

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Aside from etymology, one could argue that the maths and literary senses of lowest common denominator are somewhat opposed: the maths sense seeks a number at least as 'great' as the inputs, whereas the literary sense references a 'low' point among the character traits of the people involved.

Here's a definition from ODO:

Lowest Common Denominator noun, derogatory 2 The level of the least discriminating audience or consumer group: they were accused of pandering to the lowest common denominator of public taste - ODO

The term lowest common denominator is used in a non-mathematical context to indicate the relevant 'thing' (denominator) that all the people under discussion have in common. It's not normally used quantitatively (e.g. salaries); it's normally reserved for derogatory qualitative comparisons (e.g. education level). It is also commonly used figuratively to describe 'low' morals, or 'depths' of crudeness - e.g. bawdy jokes that cater for the lowest common denominator.

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  • @nealmcb fair point. comment deleted. – DukeZhou Oct 3 '19 at 23:56
  • @nealmcb The OP doesn’t ask for links between the two. The mathematical sense confused the OP. Aside from etymology, one could argue that the maths and literary senses are somewhat opposed: the maths sense seeks a number at least as great as the inputs, whereas the lit sense references a low-point among the character traits of the people involved. My answer addressed the OP’s query, which was to understand the literary sense. – Lawrence Oct 4 '19 at 0:06
  • @nealmcb Stack Exchange is intended to be a knowledge base for the long haul. It doesn’t matter that answers are provided two months or even two decades after the question was posted. – Lawrence Oct 4 '19 at 0:07
  • @DukeZhou Please see my comments above. – Lawrence Oct 4 '19 at 0:08
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    @Lawrence I'm afraid I did read a bit too much into the question. Thanks for your answer. Comment deleted. But I do think including your point about the contrast in meanings is good input for the OP or anyone trying to remember the senses of the different meanings, and I'm glad there are answers that clarify that. – nealmcb Oct 4 '19 at 13:05
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Hmm. Lowest common denominator here refers to people's base instincts. It has nothing to do with class or education. It refers to the hate and other negative feelings which have driven people to vote for Trump.

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