Q:

Find $[\Bbb Z_{40} : \langle[12], [20]\rangle]$

Find $[\Bbb Z_{40} : \langle[12], [20]\rangle]$
So I believe that the question is talking about the smallest subgroup which contains $12, 20$ which I believe is $\langle 4 \rangle$ 
What next?

A:

Hint: For any subgroup $H$ of a group $G$, we have $$\lvert G\rvert=[G:H]\lvert H\rvert.$$

