The least common denominator (LCD) of two fractions is the least common multiple (LCM) of the denominators of the fractions. In other words, the least common denominator is the smallest of all the common denominators. Some examples are provided in the table below.

Fractions	Denominators	Multiples of Denominators	Common Denominators	LCM of Denominators (LCD)
$\frac{2}{3}$ and $\frac{1}{2}$	$3$ and $2$	$$\begin{array}{rl}\text{Multiples of }3\text{:}& 3,6,9,12,15,\dots \\ \text{Multiples of }2\text{:}& 2,4,6,8,10,12,\dots \end{array}$$	$6,$ $12$	$6$
$\frac{5}{6}$ and $\frac{1}{4}$	$6$ and $4$	$$\begin{array}{rl}\text{Multiples of }6\text{:}& 6,12,18,24,30,\dots \\ \text{Multiples of }4\text{:}& 4,8,12,16,20,24,\dots \end{array}$$	$12,$ $24$	$12$
$\frac{1}{4}$ and $\frac{5}{2}$	$4$ and $2$	$$\begin{array}{rl}\text{Multiples of }4\text{:}& 4,8,12,\dots \\ \text{Multiples of }2\text{:}& 2,4,6,8,10,12,\dots \end{array}$$	$4,$ $8,$ $12$	$4$

The least common denominator is used when adding or subtracting fractions with different denominators. As with fractions, rational expressions must have a common denominator to be added or subtracted. The least common denominator of two rational expressions is the least common multiple of the denominators of the fractions.