Answer

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**Hint:**First we need to find the smallest digit and greatest digit in the given number so that it is formed and it is divisible by \[3\].Also we need to know the definition of divisibility test of $3$.A number is divisible by $3$ if the sum of its digits is divisible by $3$.Using this rule and doing some calculations on it Finally we will get the required digits.

**Complete step-by-step answer:**

It is given that the given number is $\_6724$

We have to find the blank space at smallest and greatest digit and it is divisible by \[3\]

A number is divisible by \[3\] if the sum of its digits is divisible by\[3\].

Now we have to sum of digits in the given number =$\_ + 6 + 7 + 2 + 4 = \_ + 19$

Then we need to check numbers for blank space to give sum would be divisible by 3

We can see here on simplifications the digits which when added them in the result $\left( {19} \right)$ gives the final number will divisible by $3$

Hence we got the smallest digit will be $2$ which will be of the form \[26724\] and we got the greatest digit will be $8$ which will be of the form \[86724\].

**Note:**In such types of questions the key concept we have to remember is that there is always the divisibility rule of $3$ which is stated above.

After that we can easily find the smallest digit and the largest digit in the blank space for the given question.

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