$ sudo apt-get remove logwatch 

Uninstall logwatch including dependent package

If you would like to remove logwatch and it's dependent packages which are no longer needed from Ubuntu,

$ sudo apt-get remove --auto-remove logwatch 

Use Purging logwatch

If you use with purge options to logwatch package all the configuration and dependent packages will be removed.

$ sudo apt-get purge logwatch 

If you use purge options along with auto remove, will be removed everything regarding the package, It's really useful when you want to reinstall again.

$ sudo apt-get purge --auto-remove logwatch 

See Also,