N is a positive integer.

When N is divided by 3, the quotient is Q_{1} with remainder 1.

When Q_{1} is divided by 4, the quotient is Q_{2} with remainder 1.

When Q_{2} is divided by 5, the quotient is Q_{3} with remainder 1.

If Q_{1}, Q_{2}, and Q_{3} are positive integers, find the smallest possible value for N that will make all of this work.

Let’s work backwards. Let’s start with Q_{3} = 1, the smallest possible positive integer quotient.

Then Q_{2} must be 6: 6/5 = 1, remainder 1.

And Q_{1} must be 25: 25/4 = 6, remainder 1.

And N must be 76: 76/3 = 25, remainder 1.

So N = 76.