The Least Common Multiple, LCM, also known as the Lowest Common Multiple or Least Common Divisor, LCD, of two numbers is the smallest natural number that can be divided evenly by either of the two numbers
Reason:
The given parameters, starting from the runner on the outer track are;
Number of spaces covered by the runner on the outer track, n₁ = 5 spaces
Number of spaces covered by the next inner runner, n₂ = 1 space
Number of spaces covered by the next inner runner, n₃ = 3 spaces
Number of spaces covered by the next runner, n₄ = 2 spaces
The numbered spot at which all the runners will be next to one another = Required
Solution:
A spot where all the runners will be next to one another is given by the Lowest Common Multiple, LCM, of their speeds or number of spaces traveled in the same time as follows;
The LCM of 5, 1, 3, and 2 = 5 × 1 × 3 × 2 = 30
Therefore, when the first runner runs 30 spaces, we have;
[tex]Time = \dfrac{30}{5} = 6[/tex]
The time taken is 6 time units
The point the runner stops is at space 30- (30 -19) = Spot 19
The distance traveled by the runner 2 at the same time is 6 × 1 = 6
∴ The distance traveled by the runner 2 at the same time = 6 spaces
The distance traveled by the runner 3 at the same time is 6 × 3 = 18
∴ The distance runner 3 travels at the same time = 18 spaces
Runner 4 travels a distance at the same time of 6 × 2 = 12
∴ Distance runner 4 travels = 12 spaces
Therefore;
The numbered spot at which all the runners will be next to one another is spot 19
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