Ken and Hamid run around a track. It takes Ken 80 seconds to complete a lap. It takes Hamid 60 seconds to complete a lap. Ken and Hamid start running at the same time from the start line. How many laps will they each have run when they next meet on the start line?

Ken will have run 3 laps and Hamid will have run 4.

Explanation:

To find this, we first find the number of seconds that will have passed when they meet again. We use the LCM, or least common multiple, for this. First we find the prime factorization of each number:

80 = 10(8)

10 = 5(2)

8 = 2(4)

4 = 2(2)

80 = 2(2)(2)(5)(2)

60 = 10(6)

10 = 5(2)

6 = 2(3)

60 = 2(2)(3)(5)

For the LCM, we multiply the common factors by the uncommon. Between the two numbers, the common factors are 2, 2 and 5. This makes the uncommon 2, 2, and 3, and makes our LCM

2(2)(5)(2)(2)(3) = 240

This means every 240 seconds they will both be at the start line.

Since Ken completes a lap in 80 seconds, he completes 240/80 = 3 laps in 240 seconds.

Since Hamid completes a lap in 60 seconds, he completes 240/60 = 4 laps in 240 seconds.