Learn English – What does “the lowest common denominator” mean in the context other than math

idiomsmeaning-in-context

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.

Best Answer

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.