Toy cars

Paul has a collection of toy cars. He wanted to regroup them. But when he divided them into groups of three, four, six, and eight, he was always one left. Only when he formed groups of seven did he divide all toy cars. How many toy cars are 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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