There is a much easier, 3-step process that doesn't involve having to reorganize your launchpad, especially useful if you created groups of folders to organize your apps.
1. In Finder, locate the application of which there are duplicates and move it to the trash, but DO NOT empty the trash.
2. Quit the Dock process through Activity Monitor. It will restart automatically, and all references to that particular application should disappear from Launchpad. Don't worry, this is normal. Leave Activity Monitor open.
3. Place the application back in the original folder and quit the Dock process again.
When it restarts, Launchpad should be down to one reference. This has worked perfectly for me many times.
Hope this helps!
Source: Personal experience