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

Question

7898 views around the world

You can reuse this answer
Creative Commons License

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:

#1/3+1/4-1/6#

Let us observe:

Multiples of #3#: #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#
...
I hope that this was helpful.