LogMeIn remote control software cannot be removed without traces by just removing the .app icon/folder from the Application directory like you used to do with the majority of software (it will leave the finder tray icon, will attempt to start on boot, etc.).
There is an easy way using the uninstaller script to achieve this task.
1. Open the terminal :
Go > Utilities > Terminal
2. Run the following command :
sudo /Library/Application\ Support/LogMeIn/uninstaller.sh
NOTE : You will be prompted for your administrator’s credentials, just enter your password and hit enter.