(a) __6724

Add the remaining digits = 6+7+2+4 = 19

To make the number divisible by 3, the sum of its digits should be divisible by 3.

The smallest multiplier of 3 which comes after 19 is 21.

Therefore, smallest number = 21 – 19 = 2

Now,

2+3+3+3 = 8

However,

2+3+3+3 = 11

If we put 8, then the sum of the digits will be 27 and 27 is divisible by 3, the number will also be divisible by 3.

Therefore, the largest number is 8.

(b) 4765__2

Add the remaining digits = 4+7+6+5+2 = 24

To make the number divisible by 3, the sum of its digits should be divisible by 3. As we can see 24 is already divisible by 3, the smallest number that can be placed here is 0.

Now,

0+3 = 3

3+3 = 6

3+3+3 = 9

However,

3+3+3+3 = 12

If we put 9, then the sum of the digits will be 33 and as 33 is divisible by 3, the number will also be divisible by 3.

Therefore, the largest number is 9.