The least number of 4 digits which is exactly divisible by $13$ is

The correct option is D $1001$
$\Rightarrow$ Divisibility rule of $13$ : Multiply last digit with 4 and add it to remaining number in given number, result must be divisible by 13.

$\Rightarrow$ $1052\to 105+(2\times 4)\Rightarrow 113\to 11+(3\times 4)\Rightarrow 23$, 23 is not divisible by 13.

$\Rightarrow$ $1039\to 103+(9\times 4)\Rightarrow 139\to 13+(9\times 4)\Rightarrow 49$, 49 is not divisible by 13.

$\Rightarrow$ $1032\to 103+(2\times 4)\Rightarrow 111\to 11+(1\times 4)\Rightarrow 15$, 15 is not divisible by 13.

$\Rightarrow$ $1001\to 100+(1\times 4)\Rightarrow 104\to 10+(4\times 4)\Rightarrow 26$, 26 is divisible by 13.

$\therefore$ $1001$ is exactly divisible by 13.