Change Apple ID on Mac

Hi,

I set up my Mac and other devices with my email, since then i've had to change my email. As such i've changed my iphone etc onto the new email (Apple ID) with a new password.

When i try to change the Mac's Apple ID (new email) it won't accept either the new or old password, nor can i update the new email address. Everytime i go through the Prefernece, Account section etc etc it doesn't recognise the old passord so i can get past 'remove find my mac' setting.

Any idea what i can do to get the Mac in sync with my other Apple devices on the same ID account ?

Many thanks.