Grandma's Cake

What is the smallest number of pieces grandma should cut her cake into to guarantee each grandchild gets the same amount of cake and none is left over?
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Problem



Grandma bakes a cake for her grandchildren who are going to visit her.

She has forgotten whether $3$, $5$ or all $6$ of her grandchildren will visit.

She wants all of the cake to be eaten by her grandchildren and would like each grandchild to get the same amount of cake.

To prepare for all three possibilities, what is the smallest number of pieces into which she should cut the cake?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.