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

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Answer 1 · 2016-12-18T10:46:38

$LCD=90$

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

$30=2xx15=2xx3xx5$
$18=2xx9=color(white)(0)2xx3xx3$
$15=color(white)(000000000)3xx5$

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:

$LCD=2xx3xx3xx5$

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

$LCD=2xx3xx3xx5=90$

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

$1/30+1/18+1/15$

We want the LCD to be 90:

$1/30(1)+1/18(1)+1/15(1)$

$1/30(3/3)+1/18(5/5)+1/15(6/6)$

$3/90+5/90+6/90=14/90$