Imelda, susan and clara are driving go carts around a track. Imelda takes 14 min, susan takes 9 min and clara takes 10 min to drive one lap. suppose all three of them start together at a point and drive at their same speeds. after how many minutes would all three meet again?

LCM(9,10,14) = 630

To find out when all three of them would meet again, we need to determine the least common multiple (LCM) of their individual lap times.

First, let's find the prime factors of each lap time:
- Imelda: 14 = 2 * 7
- Susan: 9 = 3^2
- Clara: 10 = 2 * 5

Next, find the highest power of each prime factor needed to divide any of the given numbers:
- 2: Imelda needs 2^1, Clara needs 2^1
- 3: Susan needs 3^2
- 5: Clara needs 5^1
- 7: Imelda needs 7^1

Finally, multiply the highest power of each prime factor:
2^1 * 3^2 * 5^1 * 7^1 = 2 * 9 * 5 * 7 = 630

Therefore, all three of them would meet again after 630 minutes.