Lowest common denominator

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.

Related Topics:
Mathematics - Least common multiple - Denominator - Vulgar fraction

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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.

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

Related Topics:
Addition - Subtraction

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• 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.

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.

Related Topics:
ASCII - Computer

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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. In this regard, it is often also used to mean the dumbest people or the least sophisticated.

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

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Lowest common denominator: See also ►