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

##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##