How do you find least common demonator when it comes to complex fractions?
When trying to combine fractions, such as:
a/b + c/d
Where a, b, c, and d, are pretty much any mathematical object you like, and
b and
d are the denominators of our two fractions. You can multiply the top and bottom of each fraction with the denominators of the other fractions. In this case, we'd multiply
a and
b by the
d, the denominator of the other fraction. Similarly, we multiply
c and
d by
b, the denominator of the first fraction:
ad/bd + cb/bd
And then, you'll notice, the two denominators are exactly the same, so we can combing the fraction easily:
(ad + bc)/bd
This '
bd' is called the
common denominator, because it's a denominator that is common to both fractions. But occasionally you can get a smaller common denominator, and the smallest is called the
least common denominator. To find this, you must find the
least common multiple of the denominators. This is the smallest number that is a multiple of both denominators. For example, the multiples of 5 are 5, 10, 15, 20, 25, 30, 35..., and the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32.... The least common multiple is therefore 20, since it's the lowest number that's in both lists. That means it's also the least common denominator when combining fractions.
So basically the
least common denominator is the
least common multiple of your denominators, and that in turn is the smallest number that's a multiple of all your denominators. Alternatively, you can just multiply your denominators together to get a bigger common denominator. That's what I do
