# Toy cars

Pavel has a collection of toy cars. He wanted to regroup them. But in the division 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?

Result

n =  49

#### Solution:

$3 = 3 \\ 4 = 2^2 \\ 6 = 2 \cdot 3 \\ 8 = 2^3 \\ LCM(3, 4, 6, 8) = 2^3 \cdot 3 = 24\\ \ \\ \ \\ x_{ 1 } = LCM(3,4,6,8) = 24 \ \\ \ \\ n_{ 1 } = x_{ 1 }+1 = 24+1 = 25 \ \\ z_{ 1 } = n_{ 1 }/7 = 25/7 = \dfrac{ 25 }{ 7 } \doteq 3.5714 \ \\ \ \\ n_{ 2 } = 2 \cdot \ x_{ 1 }+1 = 2 \cdot \ 24+1 = 49 \ \\ z_{ 2 } = n_{ 2 }/7 = 49/7 = 7 \ \\ \ \\ n = n_{ 2 } = 49 \ \\ \ \\ 7%3 = 1 ... 7%4 = 3 ... 7%6 = 1 ... 7%8 = 7 \ \\ 14%3 = 2 ... 14%4 = 2 ... 14%6 = 2 ... 14%8 = 6 \ \\ 21%3 = 0 ... 21%4 = 1 ... 21%6 = 3 ... 21%8 = 5 \ \\ 28%3 = 1 ... 28%4 = 0 ... 28%6 = 4 ... 28%8 = 4 \ \\ 35%3 = 2 ... 35%4 = 3 ... 35%6 = 5 ... 35%8 = 3 \ \\ 42%3 = 0 ... 42%4 = 2 ... 42%6 = 0 ... 42%8 = 2 \ \\ 49%3 = 1 ... 49%4 = 1 ... 49%6 = 1 ... 49%8 = 1 \ \\ n = 49$

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