# Logical reasoning - lowest common multiple

On a race track are 3 cars recording average lap times of 40 seconds, 60 seconds and 70 seconds. They all start simultaneously 4 minutes ago. How much longer will the race need to continue for them all to cross the start line again at the same time?

Hi everyone,
How can this question be solved?
Thanks!

I canâ€™t seem to calculate it, are you sure this is the answer?

Thatâ€™s what I did:

Step 1: Convert all times to the same unit

• The average lap times are already given in seconds: 40 seconds, 60 seconds, and 70 seconds.
• The time since the race started is given in minutes, so we convert 4 minutes to seconds: 4 minutes * 60 seconds/minute = 240 seconds.

Step 2: Calculate how many laps each car has completed

• The number of laps completed by a car is the total time elapsed divided by the time it takes for the car to complete one lap.
• Car 1: 240 seconds / 40 seconds/lap = 6 laps
• Car 2: 240 seconds / 60 seconds/lap = 4 laps
• Car 3: 240 seconds / 70 seconds/lap = approximately 3.43 laps

Step 3: Find the least common multiple (LCM) of the lap times

• The cars will all cross the start line at the same time when the total time is a multiple of each of their lap times. This is equivalent to finding the least common multiple (LCM) of the lap times.
• LCM(40, 60, 70)

The least common multiple (LCM) of 40, 60, and 70 is 840 seconds. This means that all cars will cross the start line at the same time every 840 seconds.

Step 4: Calculate the next time all cars will cross the start line

• Since the race has already been going on for 240 seconds, we need to find out when the next time that is a multiple of 840 seconds will occur.
• This is equivalent to finding the smallest multiple of 840 that is greater than 240.

The smallest multiple of 840 that is greater than 240 is 840 seconds.

Step 5: Calculate how much longer the race needs to continue

• The race has already been going on for 240 seconds, and the next time all cars will cross the start line at the same time is at 840 seconds.
• Therefore, the race needs to continue for 840 - 240 = 600 seconds.

So, the race needs to continue for another 600 seconds, or 10 minutes, for all cars to cross the start line at the same time again.

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