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Girls in Math at Yale 2021 Problem 11: Min Plus Max Volumes

Source:

February 27, 2021
Yalecollegegeometry3D geometryprism

Problem Statement

A right rectangular prism has integer side lengths aa, bb, and cc. If lcm(a,b)=72\text{lcm}(a,b)=72, lcm(a,c)=24\text{lcm}(a,c)=24, and lcm(b,c)=18\text{lcm}(b,c)=18, what is the sum of the minimum and maximum possible volumes of the prism?
Proposed by Deyuan Li and Andrew Milas
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