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What is the difference between "Login OTPs" and "Recovery OTPs"?
Login OTPs can be generated on this page: https://lastpass.com/otp.php and they are "one time passwords" that you can print off and carry with you. Each one time password in that list can then be used to log in to LastPass via https://lastpass.com/otp.php - the idea is that if you are on an untrusted computer, and do not want to enter your Master Password because of a keylogger threat, you can use the OTP. It expires after you use it, but allows you to log in without entering your Master Password. These are portable, and are not local to the device where they are generated. The list can be accessed anywhere when you log in at https://lastpass.com/otp.php where you can generated and print more. They are not to be used for account recovery.
Users do not have direct access to recovery OTPs. These are bits of data that are stored automatically by the browser add-on. When you use the LastPass browser add-on, the add-on generates this OTP and stores it in the browser. It will stay there until you go through account recovery in that specific browser where the OTP was generated and stored. If you do the recovery process (https://lastpass.com/recover.php) it will try to "call up" that OTP, and allow you to immediately reset your password if it detects that the OTP was stored in the browser.
OTPs are local to specific browsers and one OTP should be generated for each browser, on each computer, where you use LastPass. The recovery OTPs are not portable, they are stored in the specific browser's file, so recovery can only be done on a browser where you have used your LastPass account before. Like login OTPs, though, recovery OTPs will expire after they have been used once. When you next log in to your account after you've reset your Master Password, new OTPs are generated for the browser.