Henry Ernest Dudeney/Modern Puzzles/30 - The Staircase Race

Modern Puzzles by Henry Ernest Dudeney: $30$

This is a rough sketch of a race up a staircase in which $3$ men took part.

Ackworth, who is leading, went up $3$ risers at a time, as arranged;

Barnden, the second man, went $4$ risers at a time,

and Croft, who is last, went $5$ at a time.

Undoubtedly Ackworth wins.

But the point is,

How many risers are there in the stairs, counting the top landing as a riser?

I have shown only the top of the stairs.

There may be scores, or hundreds, of risers below the line.

It was not necessary to draw them, as I only wanted to show the finish.

But it is possible to tell from the evidence the fewest possible risers in that staircase.

Can you do it?

1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Locomotion and Speed Puzzles: $30$. -- The Staircase Race
1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Speed & Distance Puzzles: $58$. The Staircase Race