73 is Smallest Number whose Period of Reciprocal is 8

Theorem
$73$ is the first positive integer the decimal expansion of whose reciprocal has a period of $8$:
 * $\dfrac 1 {73} = 0 \cdotp \dot 01369 \, 86 \dot 3$

Proof
From Reciprocal of $73$:

Counting the digits, it is seen that this has a period of recurrence of $8$.

It remains to be shown that $73$ is the smallest positive integer which has this property.