# How do you find the LcD of the fractions with the following denominators: 30, 18, and 15?

##### 1 Answer

$L C D = 90$

#### Explanation:

To find the LCD, I like to first do a prime factorizations:

$30 = 2 \times 15 = 2 \times 3 \times 5$
$18 = 2 \times 9 = \textcolor{w h i t e}{0} 2 \times 3 \times 3$
$15 = \textcolor{w h i t e}{000000000} 3 \times 5$

The LCD will have all the elements that each of the denominators have.

First we have 2's. Both the 30 and the 18 have a 2, so we put in one:

LCD=2xx?

Next to 3's. The 18 has two of them and so we put in two:

LCD=2xx3xx3xx?

Now to 5's. Both the 30 and the 15 have one, so we put in one:

$L C D = 2 \times 3 \times 3 \times 5$

There are no other primes to include, so we can now multiply it out:

$L C D = 2 \times 3 \times 3 \times 5 = 90$

So let's try it out - let's say we're doing:

$\frac{1}{30} + \frac{1}{18} + \frac{1}{15}$

We want the LCD to be 90:

$\frac{1}{30} \left(1\right) + \frac{1}{18} \left(1\right) + \frac{1}{15} \left(1\right)$

$\frac{1}{30} \left(\frac{3}{3}\right) + \frac{1}{18} \left(\frac{5}{5}\right) + \frac{1}{15} \left(\frac{6}{6}\right)$

$\frac{3}{90} + \frac{5}{90} + \frac{6}{90} = \frac{14}{90}$