Question

You are helping Folsom's city manager adjust traffic patterns for the new residents south of Hwy 50. A traffic light changes every 30 seconds. Another traffic light changes every 40 seconds. Both lights just changed. After how many minutes will both lights change at the same time again? (Hint - find the LCM of 30 and 40.) Why does your answer make sense?

Answer 1

120 minutes

Yes my answer makes sense

Explanation:

This question has to do with Lowest Common Multiples

1) After how many minutes will both lights change at the same time again?

Step 1

We would find and list multiples of each number until the first common multiple is found.

Multiples of 30:

30, 60, 90, 120, 150, 180

Multiples of 40:

40, 80, 120, 160, 200

Step 2

The first common multiple of 30 aand 40 is the lowest common multiple.

Therefore,

LCM(30, 40) = 120

Therefore, both lights will change at the same time after 120 minutes.

2) Why does your answer make sense?

Lowest common multiple is a methodology used in mathematics to show the relationship between two numbers based on their multiples.

My answer makes sense because the only way both traffic light would come up at the same time can only be determined using the methodology of Lowest Common Multiple.

Hence, both lights will change at the same time after 120 minutes.