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I have a Late 2006 MacBook with the Model Number A1181. I am going to be replacing the logic board and I was wondering if I need to worry about the serial number. If I do, can I write the serial number myself or should I take it to Apple? I read that if you take the computer to them, they can write the original serial number.

Yes, Apple does have software that can write or change a serial number. But the logic board you are installing most likely already has a serial number unless it’s a brand new one that never been used and those usually only come from Apple.