Racing track

On the racing track circling three cars. The first passes one circuit for 8 seconds, the second for 20 seconds and a third for 8 seconds.

a) Calculate number of seconds since the start to catch all three cars together for the first time again across the start line?

b) How many laps ran each car until catch all three cars together for the first time?

Result

a =  40 s
1.:  5
2.:  2
3.:  5

Solution:

$a = LCM(8, 20, 8) = 40 \ \text{s} \ \\ 8 = 2 \cdot 2 \cdot 2 \ \\ 20 = 2 \cdot 2 \cdot 5 \ \\ \ \\ \text{LCM}(8, 20) = 40 \ \\ 40 = 2 \cdot 2 \cdot 2 \cdot 5 \ \\ 8 = 2 \cdot 2 \cdot 2 \ \\ \ \\ \text{LCM}(40, 8) = 40$
$1. .... 40/8 = 5$
$2. .... 40/20 = 2$
$3. .... 40/8 = 5$

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