The differences between the two types of solving these equations is that when you solve with a CD that isn't the LCD, you must simplify the equation afterward. While sometimes you must do that while solving with LCD, you will always have to if you solve with any other CD. For example, adding 1/2 and 1/3 using the LCD (6) will get you 3/6 + 2/6 = 5/6. No simplifying. Using 12 as the CD, you get 6/12 + 4/12 = 10/12 which you have to simplify into 5/6.
