What is the largest subgroup of Z contained in 10Z and 2Z? I know this is really easy but I can't find anything to confirm my answer in any notes and the fact this is 4 marks throws me off.
Is it simply just 2Z? As 10Z is just the integers that are multiples of 10 and 14Z multiples of 14? 

The other way around:  $10\Bbb Z\subset 2\Bbb Z$.
In general it would be $\operatorname{lcm}(m,n)\Bbb Z$ is the largest subgroup of $m\Bbb Z$ and $n\Bbb Z$.
