G7.2 When the positive integer $N$ is divided by $6,5,4,3$ and 2, the remainders are $5,4,3,2$ and 1 respectively. Find the least value of $N$.
Reference: 1990 HI13, 2013 FG4.3
$N+1$ is divisible by $6,5,4,3$ and 2 .
The L.C.M. of $6,5,4,3$ and 2 is 60 .
$\therefore$ The least value of $N$ is 59 .