A blue neon light blinks every 4 seconds. A red one blinks every 5 seconds while a green one blinks every 6 seconds. How many times will they blink together in half an hour?



To solve the problem, we need to determine how often the blue, red, and green neon lights blink together. This can be done by calculating the least common multiple (LCM) of their blinking intervals.

- The blue light blinks every 4 seconds.
- The red light blinks every 5 seconds.
- The green light blinks every 6 seconds.

### Step 1: Calculate 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 found by taking the highest powers of all prime factors:
\[
LCM(4, 5, 6) = 2^2 \times 3^1 \times 5^1 = 60 \text{ seconds}
\]
So, the lights blink together every 60 seconds.

### Step 2: Determine how many times they blink together in 30 minutes
Since 30 minutes equals 1800 seconds, we divide 1800 by 60 to find how many times the lights blink together:
\[
\frac{1800}{60} = 30
\]
Thus, the lights will blink together **30 times** in half an hour.

Would you like more details or have any questions?

### Relative Questions:
1. How would the solution change if the blue light blinked every 3 seconds?
2. What would happen if the green light blinked every 8 seconds?
3. Can you find the total number of individual blinks for each light in 30 minutes?
4. How do you compute the least common multiple for larger sets of numbers?
5. How would the scenario change if you were asked about blinking together in an hour?

### Tip:
Always break down the problem into manageable steps—like finding the LCM first—when solving such multi-part problems!

A blue neon light blinks every 4 seconds. A red one blinks every 5 seconds while a green one blinks every 6 seconds. How many times will they blink together in half an hour?

Discover how to calculate how many times blue, red, and green neon lights blink together in 30 minutes. This problem involves finding the least common multiple of 4, 5, and 6, suitable for students in Grades 6-8.

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