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

Question

4 years ago

14

arrive at Union Station at the same time again?

1 answer:

Dmitry_Shevchenko [17] · Answer 1 · 2021-11-27T03:05:20+03:00

Answer:

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

Step-by-step 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.