Question: equal division of objects

You have three cakes, with diameters 15cm, 20cm and 25cm (same width). You want to share the cakes equally among your four customers. How do you do it?
What if you want the cakes sliced into the minimum total number of pieces?

The answer is to cut the cakes in half, but five pieces is the minimum.

What I want is a procedure for a more general case.

m cakes (different diameters) divided equally amongst n people. what is the minimum number of cuts or pieces to achieve this.

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