If 3 people walk around a track, one takes 6 min, one takes 9 min and one takes 12 min. How long til they meet at the start line?

What is the least common multiple of 6, 9, and 12?

3 is the LCM

No. 3 is not a multiple of any of these.

To find out how long it will take for the three people to meet again at the start line, we need to determine their common time intervals or multiples of their respective times. This is because the three people will meet at the start line only when they have completed a whole number of laps around the track.

Let's find the least common multiple (LCM) of 6, 9, and 12 to determine the time it takes for them to meet at the start line.

Step 1: List the multiples of each person's time:
- The person who takes 6 minutes: 6, 12, 18, 24, 30, ...
- The person who takes 9 minutes: 9, 18, 27, 36, ...
- The person who takes 12 minutes: 12, 24, 36, ...

Step 2: Find the smallest number that appears in all three lists. In this case, it is 18.

Therefore, the three people will meet at the start line after 18 minutes.

In summary, it will take 18 minutes for the three individuals to meet again at the start line, assuming they maintain their respective speeds and complete whole laps around the track.