We are all equal but some are more equal than others

At a birthday party, three circular cakes have to be cut by vertical straight lines cuts into 34 pieces and divided among 34 excited children.

If each cake has to be cut by at least two cuts, what is the minimal number of straight line cuts needed to ensure that each child gets a (not necessarily identical) piece of cake?

Note: We can't stack up the cakes.


Image Credit: Wikimedia SimonJamesKent.
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