Solve $660x\equiv 1$ mod $43$

Question

Solve $660x\equiv 1$ mod $43$

I found $660\equiv 15$ mod $43$

So I want to solve $15x\equiv 1$ mod $43$

I tried some low numbers but none of them worked. I'm not sure what to do now.

Answer 1

Here's one way:

$15\times3=45\equiv2\bmod 43$

$2\times 22=44\equiv 1\bmod 43$

Therefore

$15\times 3\times22\equiv 1 \bmod 43$

$15\times 66\equiv1\bmod 43$

$15\times 23\equiv 1 \bmod 43$