The smallest positive integer greater than $1$ that leaves a remainder of $1$ when divided by $4$, $5$, and $6$ lies between which of the following pairs of numbers? 
选项为:A:$$2$$ and $$19$$  B:$$20$$ and $$39$$  C:$$40$$ and $$59$$  D:$$60$$ and $$79$$  E:$$80$$ and $$124$$  请回答其中一个选项.