Lowest common denominator

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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 <math>\left\{ \frac{1}{2}, \frac{1}{4} \right\}</math> is 4 because the least common multiple of 2 and 4 is 4. Likewise the LCD of <math>\left\{ \frac{1}{2}, \frac{1}{3} \right\}</math> is 6.

By using this (or any multiple of it) as a denominator, it enables addition, subtraction or comparison of fractions:

<math>\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}</math>;
<math>\frac{1}{2} - \frac{1}{3} = \frac{3}{6} - \frac{2}{6} = \frac{1}{6}</math>;
<math>\frac{1}{3} < \frac{2}{5}</math> since <math>\frac{5}{15} < \frac{6}{15}</math>.

[edit] 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 a media outlet has been charged with appealing to the "lowest common denominator", it means they have targeted the lowest, meanest, most basic and perhaps prurient of all possible hopes and dreams of their intended audience. See also 'sex sells'.

A third figurative use is to describe negotiations and agreements which only cover the points where everybody's previous positions coincide.

Note that in some of these cases the concept being expressed is actually closer to the related-but-different mathematical concept of highest common factor.