I have changed my Apple ID and password but when I switch on my iMac it continually tries to register on iCloud with the original ID and password. How do I overcome this problem and get the iMac to sign into iCloud with the new ones?

I have changed my Apple ID and password but when I switch on my iMac it continually tries to register on iCloud with the original ID and password. How do I overcome this problem and get the iMac to sign...
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