elementary number theory - Smallest positive integer modular congruence problem

I need help with the following problem:

Find the smallest positive integer $n$ such

that

$$x^n \equiv 1 \pmod{101}$$
for every integer $x$ between $2$ and $40$.

How can I approach this? Using Euclid's? Fermat's?

I know Fermat's says if $p$
is a prime, then $x^{p−1} \equiv 1 (\mod p)$but I don't know how or if I can apply it. As you can probably tell I'm very confused by modular congruences