Consider the following 2 subgroups of $\Bbb Z_{1260}$:
$$H_1=\langle 155\rangle, H_2 = \langle 261\rangle $$
My book claims that $135$ is the generator for $H_1 \cap H_2$
How can I discover that?
The $\gcd$ of $155$ and $261$ is $1$ and not $135$ ... every number is a multiple of $155$ and $261$ iff it is a multiple of their ${\rm lcm}$