Question

On a 100 feet circular race track there are lights

every 3 feet on the inner track, every 6 feet in the
middle track and every 9 feet on the outer track.
How often will the lights be at the same distance?

Answer 1

Every 18 feet.

Explanation:

1. Find the LCM between the numbers.

LCM stands for "least common multiple", and is the least number that results from multiplicating any of the 3 numbers by another number.

Analyze numbers starting from 9 to find the LCM. The first number than can be divided by 3, 6, and 9 is 18. Hence, 18 is out LCM

2. Interpret the results.

18 as a LCM means that every 18 feet there will be lights at the same distance in the circular road.

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Check out the attched image to see a linear graphic representation of the problem.