Replace @ by the smallest digit so that 723@56@ is divisible by 6.

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A number is divisible by 6 if it is divisible by both 2 and 3.
### Step 1: Divisibility by 2 The number 723@56@ must end with an even digit. So, the last @ must be 0, 2, 4, 6, or 8.
### Step 2: Divisibility by 3 The sum of the digits must be divisible by 3.
Let the first @ be x and the last @ be y. The number becomes:
7 2 3 x 5 6 y
Sum of known digits: 7 + 2 + 3 + 5 + 6 = 23
So, total sum = 23 + x + y
Since y must be even, try the smallest even digits.
Try x = 0, y = 0: Sum = 23 + 0 + 0 = 23 (not divisible by 3)
Try x = 0, y = 2: Sum = 23 + 0 + 2 = 25 (not divisible by 3)
Try x = 0, y = 4: Sum = 23 + 0 + 4 = 27 (divisible by 3)
So, x = 0 and y = 4 works.
But we are asked for the smallest digit that can replace @ in both places.
Try x = 2, y = 2: Sum = 23 + 2 + 2 = 27 (divisible by 3)
Since 2 is smaller than 4 and works for both positions, it is the smallest possible digit.
### Final Answer: The smallest digit that can replace @ so that 723@56@ is divisible by 6 is **2**.

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