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 fractions. It simplifies adding, subtracting, and comparing fractions.

The least common denominator of a set of fractions is the least number that is a multiple of all the denominators: their least common multiple. The product of the denominators is always a common denominator, as in:

but it's not always the least common denominator, as in:

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: ${\displaystyle {\frac {5}{12}}+{\frac {11}{18}}={\frac {90}{216}}+{\frac {132}{216}}={\frac {222}{216}}}$.

With variables rather than numbers, the same principles apply:

Some methods of calculating the LCD are at Least common multiple#Computing the least common multiple.

The same fraction can be expressed in many different forms. As long as the ratio between numerator and denominator is the same, the fractions represent the same number. For example:

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