Katana VentraIP

Lowest common denominator

In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions.

Practical uses[edit]

The LCD has many practical uses, such as determining the number of objects of two different lengths necessary to align them in a row which starts and ends at the same place, such as in brickwork, tiling, and tessellation. It is also useful in planning work schedules with employees with y days off every x days.


In musical rhythm, the LCD is used in cross-rhythms and polymeters to determine the fewest notes necessary to count time given two or more metric divisions. For example, much African music is recorded in Western notation using 12
8
because each measure is divided by 4 and by 3, the LCD of which is 12.

Colloquial usage[edit]

The expression "lowest common denominator" is used to describe (usually in a disapproving manner) a rule, proposal, opinion, or media that is deliberately simplified so as to appeal to the largest possible number of people.[3]

Anomalous cancellation

Greatest common divisor

reverses the process of adding fractions into uncommon denominators

Partial fraction decomposition