a, b and c are three different positive integers. What is the smallest possible value of a2b3c?

Question

This is a power and indices problem from a collins connect textbook (GCSE Frameworking Edexcel)

Answer 1

Minimize a²b³c, if a, b, c are three different positive integers.

 

  For positive integers, b³ grows faster than a² and c.

 

      Let b = smallest positive integer = 1

 

  For positive integers > 1, a² grows faster than c.

 

      Let a = 2 and c = 3.

 

If a, b, c are three different positive integers, then the smallest value of a²b³c is 2²1³(3) = 12.