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

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Answer 1 · 2014-11-02T13:44:42

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

Example
Find the least common denominator to compute:

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

Let us observe:

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

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

Hence,

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