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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 positive integer that is a multiple of the denominators. For instance, the LCD of

$\left\{ \frac{5}{12}, \frac{11}{18} \right\}$

is 36 because the least common multiple of 12 and 18 is 36. Likewise the LCD of

$\left\{ \frac{5}{6}, \frac{1}{4} \right\}$

is 12. Using the LCD (or any multiple of it, such as the product of the denominators) as a denominator enables addition, subtraction or comparison of fractions:

$\frac{5}{6} - \frac{1}{4} = \frac{10}{12} - \frac{3}{12} = \frac{7}{12};$

$\frac{1}{2} - \frac{1}{3} = \frac{3}{6} - \frac{2}{6} = \frac{1}{6};$

$\frac{7}{9} < \frac{19}{24}\text{ since }\frac{112}{144} < \frac{114}{144}.$

The lowest common denominator of two vulgar fractions can be found by calculating the least common multiple of their denominators.

Some K-12 math standards such as the latest revision of the NCTM math standards and reform mathematics textbooks created since the 1990s de-emphasize or omit coverage of the LCD entirely in favor of finding any common, but not necessarily the lowest common denominator, or by using less powerful methods such as fraction strips or "benchmark" fractions. The "cross-multiply" method of comparing fractions effectively creates a common denominator by multiplying both denominators together.

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.

The phrase is also used to describe the most basic, least sophisticated level of taste, sensibility, or opinion among a group of people. This is most often used in criticism of art, products or media thought to be aiming itself at such a group, the implied complaint usually being that the subject has been simplified to appeal to a wider audience.

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 greatest common divisor.

Lowest common denominator.html

Figurative uses

See also