SOLUTION: three buses leave at intervals of 15 minutes, 20 minutes and 25 minutes respectively. Three buses left the terminal together at 0700. At what time will it be when the buses leave t

Question 615738: three buses leave at intervals of 15 minutes, 20 minutes and 25 minutes respectively. Three buses left the terminal together at 0700. At what time will it be when the buses leave the terminal together again?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
here's a method that appears to work.
you can use this to get the GCF and the LCM
http://www.purplemath.com/modules/lcm_gcf.htm
using their method, you would break each number up into its prime factors.
primes of 15 are 3 and 5
primes of 20 are 2 and 2 and 5
primes of 25 are 5 and 5
the greatest number of times that 3 is used is 1 time in 15.
the greatest number of times that 2 is used is 2 times in 20.
the greatest number of times that 5 is used is 2 times in 25.
the lcm is equal to 3 * 2 * 2 * 5 * 5 = 300
you can verify this by listing the multiples of each of these numbers and then scanning to see which is the least common one.
the multiples are:
15 = 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300
20 = 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
25 = 25 50 75 100 125 150 175 200 225 250 275 300
scan this list and you'll see that the least common multiple is 300.
check the reference.
it shows you how to find the gcf and the lcm and it works.

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