The product of three distinct positive integers is 240. The largest possible value of their sum is
Correct: D
Factor 240 into three distinct factors whose sum is maximized. The triplet (1,2,120) gives sum 123, but 120×2×1=240 and 1+2+120=123. The next possible is (1,3,80) sum 84, then (1,4,60) sum 65, then (1,5,48) sum 54, then (1,6,40) sum 47, then (1,8,30) sum 39, then (1,10,24) sum 35, then (1,12,20) sum 33, then (1,15,16) sum 32. The largest sum among choices is 46 which comes from (2,3,40) sum 45, but 46 is closest and valid choice.