I just received a pop up telling me i am infected with 3 viruses and suggesting I let the pop up do an immediate scan. It purported to be from Apple Care.

Yes it was a scam. No one can tell remotely what you have running on your computer. Apple does not send such pop ups.

Avoid phishing emails, fake 'virus' alerts, phony support calls, and other scams - Apple Support

I have experienced the same thing and continue to every time i visit my local newspaper website. How do i get rid of it?

Stop visiting the site that is generating these scam popups. Call the site manager and tell them their site contains some malicious ad or other item.

On my iPad the official looking page said I had 3 viruses, Trojan was one. It came up 3 times on Oct. 16. How to stop this?

Within the past 24 hours I have also received the pop up telling me that I have a 3-virus infection.

The best thing to do is to simply ignore it, delete it, and do not share any information with the scammers. This happens to everyone and thousands of times every day.