When you check the option to mark a device as "trusted", we create a random, unique identifier for that device. We then encrypt that ID using Windows "crypt protect data" functions, which encrypt the ID based on the user's credentials. This ensures that another user would not be able to decrypt it. We then store the encrypted ID on the hard drive, and store a hash of the ID on our server in a database. This is passed back after the user tried to login - the hash is compared with the hash of the ID after it has been decrypted (after the user enters their email address + master password). If they match, LastPass then skips the prompt for a multifactor authentication and logs in the user.

For mobile devices, LastPass uses the smartphones UUID rather than created a unique ID, since every smartphone has a unique UUID built in.