Depending on how those passwords are generated, they could be less than truly random and thus easier for an algorithm to guess.

Thanks a lot! Now I need to change my password at all sites I have a login...

how do you remember something like that across all of your accounts? (or do you just use lastpass)?

There are a few you need to remember, for example if you have a password manager then it would be worth memorizing one of those over the course of a few days. All the rest: use a password manager. I'd expect that not even the most brilliant 1% of this planet to have unique, 14-character random password for each account they own.

For special accounts, such as bank accounts, you could have a second password manager database with a unique password, if you are concerned that a password db which gets unlocked (almost) daily is not secure enough. Or remember unique password for those special accounts.

I store them in a password store[0], encrypted to my GPG key. That store is itself a git repo, which is encrypted to the same key using git-remote-gcrypt and synced with a remote server.

Thus I can run something like:

    $ pass foobar.example
    jDHQxFTkPjLkvbLNRQe5Ad

Or:

    $ pass -c bazquux.example
    Copied bazquux.example to clipboard. Will clear in 45 seconds.

[0] https://www.passwordstore.org/

One does not try to "remember" those. One uses a password manager, it does the remembering, and you only have to remember the one long password that unlocks the manager.

There is a chicken and egg problem. How does one make a secure password manager password...? There still is the need for users to learn how to generate secure but memorizable passwords.

With one big exception. There is only one (not 30 or 50 or 100) to have to remember (the master one) and it is one that someone will have to enter repeatedly (until they decide to change it) so they will eventually have enough practice to actually remember it.