Wasn't sure exactly which forum this fit in, and I greatly apologize if it's in the wrong one.
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I just got hired to maintain about 40 websites with more being added to the list everyday.

All the websites have the same directory/file structure as they all use the same script.

I found a bug in the script and needed to modify several core files to fix the bug. Right now I'm logging into each website manually via FTP but it's taking to long to do this on an individual basis.

Here is my question, how can I upload or how should I go about updating these 40 websites with the newly modified files in a streamlined process instead of doing it one by one?

A. All websites except for about 10 or so are on the same dedicated server which I have root access to. The server is CentOS with CPanel installed.

B. Every website is on it's own separate hosting account on the server.

C. I have FTP access to every website.

Thank you in advance for taking the time to read this and reply.