It's possible to block Logmein for your internal network
If you would like to prevent your employees from installing LogMeIn on their work computer, you should block secure.logmein.com on your firewall(s).
If you are on a Windows Domain, you may also install a Group Policy Object, which will allow you to limit access throughout your entire domain, without the need for firewall rules. Please see the link below for more information regarding the Group Policy Object.
https://logmeinsupport.com/kblive/crm/selfservice/displaywh.jsp?DocId=2538Let me know if it works for you