Question

If three positive integers a b c are in ap such that abc = 8

Answer 1

For a set of positive numbers, the arithmetic mean is never smaller than the geometric mean. The geometric mean of the three numbers is 3√8=2. Since the numbers are in AP, their arithmetic mean is b. Thus the smallest possible value for b is 2 (this is achievable when all three numbers are 2 - an AP with zero common difference)