Thee consecutive Odd Numbers can be taken as n-2, n, n+2

So, their sum becomes n-2 + n + n +2 = 3n
=> Sum of three consecutive odd numbers should be a multiple of 3

Divisibility rule of 3 is Sum of all the digits of the number should be divisible by 3
Let's check all the options choices now

(A) 15 -> Sum of digits = 1+5 = 6 => Divisible by 3 => POSSIBLE

(B) 75 -> Sum of digits = 7+5 = 12 => Divisible by 3 => POSSIBLE

(C) 123 -> Sum of digits = 1+2+3 = 6 => Divisible by 3 => POSSIBLE

(D) 297 -> Sum of digits = 2+9+7 = 18 => Divisible by 3 => POSSIBLE

(E) 313 -> Sum of digits = 3+1+3 = 7 => NOT Divisible by 3 => NOT POSSIBLE

So, Answer will be E
Hope it helps!

Watch the following video to learn the Basics of Divisibility Rules