The problem: Find the smallest positive integer $x$ such that
$x$ divided by $4$ has remainder $1$
$x$ divided by $5$ has reminder $2$
$x$ divided by $6$ has remainder $3$
Now, my first idea was to add to each divisor its the remainder and multiply the quantities obtained.
But $315$ does not satisfy all the conditions above, and I don't know how to get the smallest integer that satisfies the conditions. Any help?