Repeated Division w/Remainders

N is a positive integer.
When N is divided by 3, the quotient is Q1 with remainder 1.
When Q1 is divided by 4, the quotient is Q2 with remainder 1.
When Q2 is divided by 5, the quotient is Q3 with remainder 1.
If Q1, Q2, and Q3 are positive integers, find the smallest possible value for N that will make all of this work.


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Let’s work backwards. Let’s start with Q3 = 1, the smallest possible positive integer quotient.

Then Q2 must be 6: 6/5 = 1, remainder 1.

And Q1 must be 25: 25/4 = 6, remainder 1.

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

So N = 76.

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