Haven't used Logmein in ages but i'd check if it keeps an activity log.

Look for folders accessed and how long logmein was active.

There are sites that will tell you if your accounts and passwords have been hacked, they usually also offer a list of (former hopefully) passwords of yours.

Also, check in your browsers for saved passwords. Those are the ones that would worry me in the first place. They might be out in the wild now.

Kill, nuke, dissapear Logmein from your computers. If you are a paying customer log a complaint with them.

0-0

You seem to be making a lot of assumptions.

If you don't know how to properly assess the situation then by all means nuke it.
Although I have never ever had to nuke any system for a malware/AV issue except for a confirmed Ransomware detection.

Sometimes "fake alerts" pop up due to java malware.
I have seen plenty of phishing expeditions where an email may actually mention a password used.
This is generally from a hack on some online site with poor security but they make you think they hit your computer.

Unless you have enabled some "listening" mode for LOGMEIN (Teamviewer,etc) or forwarded ports for MS RDP AND have used the same PW mentioned then it is unlikely this is just a ploy to get you to bite into trouble.

However, using good common sense and closing these holes, changing PS's, running a good AV scan such as MalwareBytes, uninstalling all remote listening apps would most likely go a long way.
Also don't leave any critical data on the computer IE: Excel of PW's, or Account numbers or list of online PW/usernames, etc.