# How do you find the least common denominator for rational expressions?

Nov 2, 2014

The least common denominator is the least common multiple of denominators.

Example
Find the least common denominator to compute:

$\frac{1}{3} + \frac{1}{4} - \frac{1}{6}$

Let us observe:

Multiples of $3$: $3 , 6 , 9$, 12,$15 , \ldots$
Multiples of $4$: $4 , 8$,12, $16 , \ldots$
Multiples of $6$: $6$,12,$18 , \ldots$,

So, the least common multiple of $3$,$4$, and $6$ is $12$.

Hence,

$\frac{1}{3} + \frac{1}{4} - \frac{1}{6} = \frac{4}{12} + \frac{3}{12} - \frac{2}{6} = \frac{4 + 3 - 2}{12} = \frac{5}{12}$
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I hope that this was helpful.