Suppose the length of the stick is 60.
Marked in red, each segment is 60/ 10=6.
Yellow mark, each segment is 60/ 12=5.
Blue mark, each segment is 60/ 15=4.
The least common multiple of 6,5 is 30,60/30 = 2.
That is, the red and yellow marks have two repetitions, except the last 1, and there are 1 repetitions in the middle.
The least common multiple of 5,4 is 20,60/20 = 3, except for 1 at the end, and there are two repeated marks in the middle.
The least common multiple of 6,4 is 12,60/1 2 = 5, except the last1,and there are four repeated marks in the middle.
A * * * in the middle of the mark is:
( 10- 1)+( 12- 1)+( 15- 1)- 1-2-4 = 27.
A stick is divided into 27+ 1=28 segments.