Feeds from multiple blogs into WordPress

I have a project which I would like to develop.  What I have in mind is setting up feeds from two or more blogs (the source blogs) into a WordPress blog such that as new posts are published to those source blogs, they appear in the WordPress blog as if they were posted there in the first place.  In other words, I am looking for a way to consolidate the feeds from some of my other blogs into one of my main blogs.

Does anyone know how to do this?

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