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MathNet 2012 Question 2

Math Olympiad Vault · MathNet 2012

Question 2

David is a very curious child. He has a container in the shape of a rectangular cuboid such that its three dimensions (width, height and depth) are different positive integers. The container is filled with two different unmixable liquids, $A$ and $B$, and the volume of $A$ is $36\%$ of the volume of $B$.

David observes that, when laying the recipient on any of its six faces, the height that each liquid reaches is a positive integer.

Which is the smallest possible volume of David's container?

Illustrative configuration only.

Question illustration