Question

At union station, you notice that three subway lines just arrived at the same time. How long must you wait until all three lines arrive at Union Station at the same time again?

Answer 1

You must wait 60 minutes for all three lines to arrive at Union Station at the same time again.

Explanation:

The complete question in the attached figure

Step 1

Find the least common multiple (LCM) of the three numbers

List the prime factors of each number

`10=(2)(5)\\12=(2^2)(3)\\15=(3)(5)`

Multiply each factor the greatest number of times it occurs in any of the numbers to find out the LCM

The LCM is equal to

`(2^2)(3)(5)=60`

therefore

You must wait 60 minutes for all three lines to arrive at Union Station at the same time again.