The least number of 4 digit which is exactly divisible by 7 is :

1. 1,015

2. 1,008

3. 1,001

4. 1,022

The smallest 4-digit number = 1000.

$\begin{array}{l} \phantom{x^2 }{142} \ 7\overline{\smash{\big)}1000} \ \phantom{x}\phantom{}\underline{-7} \ \phantom{{x^2))}} 30 \ \phantom{{x} )}\underline{-28} \ \phantom{{x^2 } + } 20 \ \phantom{{x} ))}\underline{-14} \ \phantom{{x^2 +)}} 6 \ \end{array}$

Quotient = 142

Remainder = 6

“To get the next multiple of 7, we add (7 − remainder) to 1000.”

Next multiple = 1000 + (7 − 6)

= 1000 + 1

= 1001.

Therefore, the least 4-digit number exactly divisible by 7 is 1,001.

Hence, option 3 is the correct option.