Method I:

As the number comprising of all 1's is obtained on multiplication by 7, so it means that 7 is the factor of that number.

Our answer will the smallest number comprising of all 1's that will be divisible by 7. So, let's check. Is 1 divisible by 7? – No Is 11 divisible by 7? – No Is 111 divisible by 7? – No Is 1111 divisible by 7? – No Is 11111 divisible by 7? – No Is 111111 divisible by 7? – Yes So, $111111/7 = 15,873$

Method II:

Multiply the numbers given in the options by 7, and see which multiplication gives you a resultant comprising of all 1's.

Checking option (D):

$15873 \times 7 = 111111$