Concept:A number is divisible by 3 if the sum of its digits is divisible by 3.Explanation:First, let's find the sum of the digits of the given number 321727.Sum of digits = $3 + 2 + 1 + 7 + 2 + 7 = 22$.Now, we need to find the smallest number to add to 321727 so that the new sum of digits is divisible by 3. We look for the next multiple of 3 greater than 22.The multiples of 3 are ..., 18, 21, 24, 27, ...The next multiple of 3 after 22 is 24.To get a sum of 24, we need to add a number to 22.Number to add = $24 - 22 = 2$.So, if we add 2 to the original number, the sum of its digits will be 24, which is divisible by 3. Therefore, the resultant number will be exactly divisible by 3.Answer:2The correct option is C.