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.