SOLUTION: Three taxi cabs make a complete trip from downtown to the airport and back in 15, 39, and 65 minutes, respectively. If all three cabs leave at the same time, what is the shortest t

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Three taxi cabs make a complete trip from downtown to the airport and back in 15, 39, and 65 minutes, respectively. If all three cabs leave at the same time, what is the shortest t      Log On


   

Question 726105: Three taxi cabs make a complete trip from downtown to the airport and back in 15, 39, and 65 minutes, respectively. If all three cabs leave at the same time, what is the shortest time that must pass before they are all together again?
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
In order to find the shortest time when they are back at the same point, we need to find the least common multiple of the 3 trip times. To find the LCM, factor each number and express as powers of primes:
15 = 3*5
39 = 3*13
65 = 5*13
Now multiple the highest power of each prime nunber together:
LCM = 3*5*13 = 195
So the 1st cab makes 195/15 = 13 round trips
The 2nd cab makes 195/39 = 5 trips
And the 3rd cab makes 195/65 = 3 trips
Ans: 195 minutes