The line a bus arrives at the bus stop every 25 minutes, and the line b bus arrives every 15 minutes. Both are at the stop right now. On how many will both be at the bus stop again

after 75 minutes

Step-by-step explanation:

The least common multiple (LCM) of 15 and 25 is 75. It can be found a couple of ways:

1. List the factors of each number and find the product of the unique ones:

15 = 3·5

25 = 5²

The LCM is 3·5² = 75.

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2. Find the greatest common divisor (GCD) and divide the product of the numbers by that value. From the above list of factors, we see that 5 is the GCD of 15 and 25. Then the LCM is ...

15·25/5 = 75

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Or, you can simply list multiples of each number and see what the smallest number is that is in both lists:

15, 30, 45, 60, 75, 90

25, 50, 75, 100

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The two buses will appear together again after 75 minutes.