Question

LCD of 3/15, 15/21, 7/8? I need to know the steps, not just the answer please. Thank you!

Answer 1

$\cfrac{3}{15},\quad \cfrac{15}{21},\quad \cfrac{7}{8}\impliedby \cfrac{}{LCD}$
LCD or least common divisor simply means, 
"a number, that has all those denominators as factors"
a good example of that will be the obvious
15 * 21 * 8 = 2520
we know 2520 is a CD a common divisor, because it has them all :)
we just put them all there anyway
but is not an Least CD per se
there may be a smaller one, that contains all
let us see hmmm how about 840 :)

so... 2520 is a valid CD, just not the smallest possible
840 would be the Least CD then

$\cfrac{3}{15},\quad \cfrac{15}{21},\quad \cfrac{7}{8} \\ \quad \\ \begin{array}{llll} 15&|&3\\ 5&|&5\\ 1 \end{array}\impliedby \textit{so, 15 has factors of 3 and 5} \\ \quad \\ \begin{array}{llll} 21&|&3\\ 7&|&7\\ 1 \end{array}\impliedby \textit{so, 21 has factors of 3 and 7} \\ \quad \\ \begin{array}{llll} 8&|&2\\ 4&|&2\\ 2&|&2\\ 1 \end{array}\impliedby \textit{so 8 has 3 factors, 2 all of them}$

15 and 21, share a common factor of 3
so we'll use that once, so instead of using 3 * 5 * 3 * 7
we'll use 3 * 5 * 7 only

now, onto 8, 8 has three 2's, neither 15 or 21 share a 2 so, we'll use all
so, we end up with 3 * 5 * 7 * 2 * 2 * 2 as our LCD
which is 840

the procedure to pluck out the factors, is called "prime factoring", as you see above,

you start by dividing by 2, till you can't, then by 3, till you can't, then by 5, till you can't

we don't do 4, because if anything is divisible by 2, well, is also divisible by 4

and then you continue if there's more left, you divide by 7 till you can't

we don't do 6, because 6 is 2 * 3, is anything is divisible by 6, it'd had already come out in our division by 2 and 3
and so on

Answer 2

First, I would reduce 3/15 and 15/21 to simplest form.
1/5, 5,7 

You could list multiples of all your denominators. But in this case, because two of your denominators are already prime (5 and 7), you can just multiply the three denominators together.

5 x 7 x 8 
This will give you the LCD