Toy cars

Pavel has a collection of toy cars. He wanted to regroup them. But in the division in groups of three, four, six, and eight, he was always one left. Only when he formed groups of seven he divided everyone. How many toy cars have in the collection?

Correct answer:

n =  49

Step-by-step explanation:

$$\begin{gathered} 3...\text{ prime number} \\ 4=2^2 \\ 6=2\cdot 3 \\ 8=2^3 \\ LCM(3,4,6,8)=2^3\cdot 3=24 \\ {x}_1=LCM(3,4,6,8)=24 \\ {n}_1=x_1+1=24+1=25 \\ {z}_1=n_1/7=25/7=\frac{25}{7}=3\frac{4}{7}\doteq 3.5714 \\ {n}_2=2\cdot x_1+1=2\cdot 24+1=49 \\ {z}_2=n_2/7=49/7=7 \\ n=n_2=49 \\ 7 \end{gathered}$$

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