Deleting is not possible, however, you can file a removal request by contacting them:
https://secure.logmein.com/contactus/
Always ask for confirmation, and check if your account really got deleted.
URLS:
http://logmein.com
Please note that AccountKiller.com is not associated with the business listed on this page. AccountKiller provides easy-to-understand instructions and guides on how to cancel charges and relationships from the list of businesses on our site, we have no affiliation with these businesses.