https://file.aiquickdraw.com/mathbot/file/1726692142981edikmkvd.jpg

The problem you provided in the image is as follows:

**Question:**
A dark neon light blinks every 4 seconds, a light one blinks every 5 seconds, and a white one blinks every 6 seconds. How many times do they blink together in one hour?

### Solution:

To solve this, we need to find how often all three lights blink simultaneously. This can be done by determining the **least common multiple (LCM)** of the blink intervals (4, 5, and 6 seconds).

#### Step 1: Finding the LCM of 4, 5, and 6
- Prime factorization of 4: \( 2^2 \)
- Prime factorization of 5: \( 5^1 \)
- Prime factorization of 6: \( 2^1 \times 3^1 \)

The LCM is the product of the highest powers of all primes involved:
\[
\text{LCM}(4, 5, 6) = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60 \text{ seconds}
\]

So, all three lights blink together every 60 seconds.

#### Step 2: Calculate how many times they blink together in one hour
- There are 60 minutes in an hour, and each minute has 60 seconds, so there are:
\[
60 \times 60 = 3600 \text{ seconds in one hour}.
\]
- Since they blink together every 60 seconds, the number of times they blink together in an hour is:
\[
\frac{3600}{60} = 60 \text{ times}.
\]

### Final Answer: 
They blink together **60 times** in one hour.

---

Let me know if you'd like more details or have further questions! Here are some additional questions to extend your understanding:

1. What is the general method to find the least common multiple (LCM) of three numbers?
2. How would the answer change if the blinking times were in minutes instead of seconds?
3. If the dark neon light blinked every 3 seconds instead of 4, how would the LCM change?
4. What is the mathematical significance of the greatest common divisor (GCD) in relation to the LCM?
5. Can you think of a real-world scenario where synchronized blinking or timing would be critical?

**Tip:** Knowing how to compute the LCM is crucial when dealing with problems involving periodic events happening at different intervals!

A dark neon light blinks every 4 seconds, a light one blinks every 5 seconds, and a white one blinks every 6 seconds. How many times do they blink together in one hour?

In this problem, we calculate how many times three lights with blinking intervals of 4, 5, and 6 seconds will blink together in one hour by finding their least common multiple (LCM). Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation