Athletes

Athletes at the stadium could enter two-steps, three-steps, four-steps, five-steps, six-steps. There were more than 100 but less than 200. How many athletes were there?

Correct result:

n₁ =  120
n₂ =  180

Solution:

$$\begin{gathered} 2\mathrm{.}\mathrm{.}\mathrm{.}primenumber \\ 3\mathrm{.}\mathrm{.}\mathrm{.}primenumber \\ 4=2^2 \\ 5\mathrm{.}\mathrm{.}\mathrm{.}primenumber \\ 6=2\cdot 3 \\ LCM(2,3,4,5,6)=2^2\cdot 3\cdot 5=60 \\ a=LCM(2,3,4,5,6)=60 \\ {x}_1=100\mathrm{/}a=100\mathrm{/}60={\displaystyle \frac{5}{3}}\doteq 1.6667 \\ {x}_2=200\mathrm{/}a=200\mathrm{/}60={\displaystyle \frac{10}{3}}\doteq 3.3333 \\ {n}_1=a\cdot \lceil x_1\rceil =60\cdot \lceil 1.6667\rceil =120 \end{gathered}$$

$n_2=n_1+a=120+60=180$

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