Question about running Bitcoin Core on 2 computers

Hi,

I have a spare 1tb portable usb hard drive, and I've decided to save the blockchain to it so that I can run Bitcoin core on my desktop. I also have a laptop.

My question is, can I run Bitcoin Core on the laptop using the same portable hard drive with the blockchain downloaded by my desktop on it? Or does each instance of Bitcoin Core have to download the blockchain separately?

Thanks!

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