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.