The smallest $7$-digit number using the digits $1,2,7,4$ is$.$

The correct option is D

$1111247$

We are looking for a smallest $7$-digit number using $1,2,7,4$

For the smallest number put $1$ at the higest plave value and then $1,1,1$ and $2$ and $4$ and at the unit place is $7$

The number will be $1111247$

Hence$,$ the smallest $7$-digit number using $1,2,7,4$ is $1111247$

therefore$,$ option $\left(D\right)$ is correct.