I am very confused on how to figure out the below math problem:

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?

Please help me.

Find the least common multiple of 30 and 40.

30, 60, 90, 120, 150
40, 80, 120, 160

The least common multiple of 30 and 40 is 120.

How did you know that I need to find the least common multiple of 30 and 40.

Would 120 be the answer? So both lights would change at the same time again after 120 minutes.

You need to know what time they'd change at the same time.

Yes, 120 is correct.

What was the indicator in the word problem is what I am trying to figure out that told you multiple?

I just thought about it. No magic tricks.

The reason why I was asking is I printed out a paper to look out for key words in math word problems.

Thank you for helping me solve the problem.

To solve this problem, you can use the concept of finding the least common multiple (LCM) of two numbers. In this case, the two numbers are 30 and 40, representing the time it takes for each traffic light to change.

To find the LCM of two numbers, you can follow these steps:

Step 1: Find the prime factorization of each number.
- The prime factorization of 30 is 2 × 3 × 5.
- The prime factorization of 40 is 2 × 2 × 2 × 5.

Step 2: Identify common factors.
- The common factors between 30 and 40 are 2 and 5.

Step 3: Multiply the common factors and the remaining factors together.
- The LCM of 30 and 40 is 2 × 2 × 2 × 3 × 5 = 120.

Therefore, both traffic lights will change at the same time again after 120 seconds, or 2 minutes.