lowest common multipul

Question

city hoppa runs two buses starting from the same bus stop. One bus has a rout that takes 25 minutes. The other bus has a route that takes 35 minutes. both buses leave the bus stop at 6.A.M and runs constantly. what is the next time the buses will be able to stop together?

Answer 1

Great job in knowing that you need to find the least common multiple.

Bus a = 25 min

Bus b = 35 min

When is bus a and bus b going to stop together?

This only happens when we have a common multiple:

So when 25 times some number (a) is equal to 35 times another number (b):

25a = 35b

Well we already know one common multiple is

25 * 35 = 35 * 25

But that's not the LEAST common multiple. So let's reduce a and b. We can divide both by 5 so let's do it:

25 * 7 = 35 * 5

175 = 175

Ok so at 175 minutes they will stop together.

How many hours are in 175 minutes?

175/ 60 = 2 hours 55 minutes

So if they start at 6am and they stop together 2 hours and 55 minutes later, it means it is 8:55am when they meet again.