G4.3 The remainders of an integer when divided by $10,9,8, \ldots, 2$ are $9,8,7, \ldots, 1$ respectively. Find the smallest such an integer.
Let the integer be $N$.
$N+1$ is divisible by $10,9,8,7,6,5,4,3,2$.
The L.C.M. of $2,3,4,5,6,7,8,9,10$ is 2520 .
$\therefore N=2520 k-1$, where $k$ is an integer.
The least positive integral of $N=2520-1=2519$