I own both a GT275 with a tiller and a LX176. I have attached pictures. The GT275 has a rear hitch that extends out several inches past the gas tank. Also the GT275 has a place to attach the special bolts that hold the tiller. (The LX has some holes, but not in the correct place for those bolts.)
Also the GT275 has an extra part of the lift mechanism to attach the bracket for the tiller. So the LX176 can not handle the tiller without several changes. Plus the GT has a transmission that is stronger to handle ground engagement. Perhaps the person you bought the tractor from was mistaken, and his dad used a different tractor to till with.