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In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the least common multiple of the denominators of a set of vulgar fractions.
It is the smallest (non-zero) number that is a multiple of the denominators. For instance, the LCD of {1/2, 1/4} is 4 because the least common multiple of 2 and 4 is 4. Likewise the LCD of {1/2, 1/3} is 6.
By using this (or any multiple of it) as a denominator, it enables addition, subtraction or comparison of fractions:
- 1/2 + 1/4 = 2/4 + 1/4 = 3/4;
- 1/2 − 1/3 = 3/6 − 2/6 = 1/6;
- 1/3 < 2/5 since 5/15 < 6/15.
Figurative uses
The term is used figuratively to refer to the "lowest"—least useful, least advanced, or similar—member of a class or set which is common to things that relate to members of that class. For instance, ASCII characters are the lowest common denominator for computers, in that this set is very limited, but practically every modern computer can interpret binary data into these characters.
Another figurative use is as a rhetorical device in criticism of mass media. When the media is charged with appealing to the "lowest common denominator", it means they targeted the lowest expectations and broadest interests of an audience with a varying range of tastes.
A third figurative use is to describe negotiations and agreements which only cover the points where everybody's previous positions coincide.
Note that in all these cases the concept being expressed is actually closer to the related-but-different mathematical concept of highest common factor.
See also
- Greatest common divisor
- Least common multiple
- Partial fraction expansion - reverses the process of adding fractions into uncommon denominators.
External links
"Lowest common denominator"