Method of searching any application installed or any file related to that on Macbook?
First off, if you just google the words uninstall logmein mac, you will find the vendor's Help entry on where to find and delete the relevant files... 

In general, it's rather difficult to track every file installed by one application installer (that is if the application files are not consequently self-contained within the .app file).

A) The Finder's Spotlight search has an option to search files by their date of addition, but the Spotlight search doesn't include Library and System folders. A better search application I would recommend instead would be Easy Find (freeware by Devon Technologies). It has extensive search options and will walk through the whole system, and includes hidden files/folders. 

B) If the application installer came as a standard installer package, a '.pkg file', you can often use the package tool Pacifist (shareware by CharlesSoft) to open it and list the contained files with their target folder locations (in Unix: directories) on the machine. Then you go to these folders in Finder (or the Terminal) and delete files/folders 'manually'. 



(Hey I'm not affiliated with any of the companies and don't get money for mentioning them or something. These apps are just tried-and-true classics on the Mac.)