Log Me In Tech support

LogMeIn is third party software. To contact Apple Support, you should head to Get Support.

What information did you give to these people?

I would strongly recommend changing any passwords associated with your Apple ID urgently.

Change your Apple ID password – Apple Support (UK)

Also, you might want to note that you have asked this question on a user-to-user forum, where we are volunteers and not Apple employees.

Additionally, if you allowed access to your computer to the scammers, I'd suggest you erase your device and reinstall from scratch (after changing all your passwords). If you shared financial information, call your bank and report possible fraud.