If a, b and c are positive integers such that ab = 432, bc = 96 and c

Question

If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is

Accepted Answer

46. Since c&lt;9 , we can have the following viable combinations for b × c = 96 b	imes\ c\ =96 b × c = 96 (given our objective is to minimize the sum): 48 × 2 48	imes\ 2 48 × 2 ; 32 × 3 32	imes3 32 × 3 ; 24 × 4 24	imes\ 4 24 × 4 ; 16 × 6 16	imes6 16 × 6 ; 12 × 8 12	imes8 12 × 8 Similarly, we c