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?


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.

  • I thought Trump said he, "knew words..." – Jim Jun 1 '16 at 2:31
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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

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
  • @tchrist - You are of course technically correct, but the non-mathematical idiom has the meaning it has. This is likely due in part to the fact that "least" can be taken to mean "most primitive". – Hot Licks Jun 1 '16 at 2:42
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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

My guess at the "try talking English" comment was that the issue was with the word demagogue ("What, you mean like Thor?").


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!"

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.

  • Unsurprising that the correct answer received no upvotes (but mine.) This idiom has historically been used in media to describe the broadest possible audience for content. This is the sense in which Hawking was using the term with no uncertainty: en.wikipedia.org/wiki/… – DukeZhou Jul 5 '18 at 18:06

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.

protected by tchrist Feb 5 '17 at 0:22

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