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.

Description

The lowest common denominator of a set of fractions is the lowest number that is a multiple of all the denominators: their lowest common multiple.

The product of the denominators is always a common denominator, as in:

: <math>\frac{1}{2}+\frac{2}{3}\;=\;\frac{3}{6}+\frac{4}{6}\;=\;\frac{7}{6}</math>

but it is not always the lowest common denominator, as in:

: <math>\frac{5}{12}+\frac{11}{18}\;=\;\frac{15}{36}+\frac{22}{36}\;=\;\frac{37}{36}</math>

Here, 36 is the least common multiple of 12 and 18. Their product, 216, is also a common denominator, but calculating with that denominator involves larger numbers:

: <math>\frac{5}{12}+\frac{11}{18}=\frac{90}{216}+\frac{132}{216}=\frac{222}{216}.</math>

With variables rather than numbers, the same principles apply:

See also

  • Anomalous cancellation
  • Greatest common divisor
  • Partial fraction decomposition, reverses the process of adding fractions into uncommon denominators

References

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