Lowest common denominator

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

The same thing also works with variables:

[math]\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} }[/math]