# Lowest common denominator

the lowest common multiple of the denominators of a set of fractions

The lowest common denominator (also least common denominator and LCD) is the least common multiple of the denominators (bottom parts) of a group of fractions. It makes it easier to add, subtract, and compare fractions.

The LCD of ${\displaystyle {\frac {1}{2}}}$ and ${\displaystyle {\frac {2}{3}}}$ is 6. This is because ${\displaystyle {\frac {1}{2}}}$ and ${\displaystyle {\frac {2}{3}}}$ equal ${\displaystyle {\frac {3}{6}}}$ and ${\displaystyle {\frac {4}{6}}}$. 6 is the smallest number that can be at the bottom of both of those fractions.

The same thing also works with variables:

${\displaystyle {\frac {1}{2x}}+{\frac {3}{x^{2}}}={\frac {1}{2x}}{\color {Green}\cdot {\frac {x}{x}}}+{\frac {3}{x^{2}}}{\color {Green}\cdot {\frac {2}{2}}}={\frac {x}{2x^{2}}}+{\frac {6}{2x^{2}}}={\frac {x+6}{2x^{2}}}}$