x = 10, y = 15, z = 30

I used guess-and-check, though...

Here's another solution:

x = 8, y = 16, z = 80

Here's a third solution (again, using guess-and-check):

x = 10, y = 12, z = 60

...and a fourth (this is fun ):

x = 12, y = 15, z = 20

01