If the number 3727x4 is completely divisible by 8, then the smallest integer in place of x will be:

According to the divisibility rule of 8, a number is divisible by 8 if the number formed by its last three digits is completely divisible by 8.
The last three digits of the given number 3727x4 form the number
7x4
, which can be written as 700+10x+4.

Let us test the given options for the smallest integer value of x:

For x=0, the last three digits form 704.
Dividing 704 by 8:

8
704
​
=88
Since 704 is exactly divisible by 8, x=0 satisfies the condition.

Since 0 is the smallest non-negative integer among the choices, it is the correct answer.