Final answer:
The sum of the least and the greatest four-digit multiples of 4 using the digits 1, 2, 3, and 4 is 5546.
Step-by-step explanation:
The question asks us to find the sum of the least and the greatest positive four-digit multiples of 4 that can be written using the digits 1, 2, 3, and 4 exactly once. To find the least multiple of 4, we need the smallest number formed with these digits that is also divisible by 4, which is 1234. To find the greatest multiple of 4, we need the largest number formed with these digits divisible by 4, which is 4312. Since both these numbers are divisible by 4, thus they are valid multiples of 4.
To find the sum, we simply add them together:
1234 + 4312 = 5546.
Therefore, the sum of the least and the greatest positive four-digit multiples of 4 using the digits 1, 2, 3, and 4 is 5546.