Here's what you should do until you get better at it:

Factor all the numbers and letters down into prime factors:

Break  all the way down far as it will go.  Write it
as 

3*3*x*x*y

Do the same with 

2*2*3*3*x*y*y*y

So you have:

3*3*x*x*y
2*2*3*3*x*y*y*y

Now line those up this way:

Line the rows of factors up so that
as many from the first row as possible
have like factors under them in the 
second row.  Only put a factor of the first
above a like factor in the bottom

    3*3*x*x*y
2*2*3*3*x  *y*y*y

Then under that draw a line and bring
all the factors down below the line,
like this:

    3*3*x*x*y
2*2*3*3*x  *y*y*y
-----------------
2*2*3*3*x*x*y*y*y

Simplify that and that's the LCM:



Later on you'll learn this shortcut:

"The LCM contains the biggest power of every letter that appears
in either expression".

Edwin