Green Line buses run every 10 minutes. Red Line buses run every 20 minutes. Purple Line buses run every 35 minutes. One bus from each Line leaves the city centre at 09 00. After how many minutes will buses from all Lines next leave the city at the same time?

Take there LCM 2 ! 10,20,352 ! 5,10,355 ! 5,5,357 ! 1,1,7- ! 1,1,1L.C.M = 2x2x5x7 = 140So, after 140 minutes the three lines will again leave at the same time.

140 minutes

Step-by-step explanation:

We can start by finding the LCM (least common multiple) of 10, 20, and 35. To do this, we can prime factorize (finding the prime factors of the number) all of the numbers.

10: 2, 5

20: 2, 2, 5

35: 5, 7

We can see that we need two 2s (20 has two 2s in its prime factorization), one 5 (all of them have one 5), and one 7 (35 has one 5 in its prime factorization) so that the LCM can be divisible by all of the numbers

2²*5*7=4*5*7=20*7=140

After 140 minutes the buses from all Lines will leave the city

36 is the final answer! : )