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 find how many times the blue, red, and green neon lights blink together in half an hour, we need to calculate the least common multiple (LCM) of their blinking intervals, then determine how many times this event occurs in 30 minutes.

1. **Blinking intervals**:
   - The blue light blinks every 4 seconds.
   - The red light blinks every 5 seconds.
   - The green light blinks every 6 seconds.

2. **Find the LCM**:
   The least common multiple of 4, 5, and 6 is the smallest number that all three numbers divide into evenly.

   \[
   \text{LCM}(4, 5, 6) = 60 \text{ seconds}
   \]

   Therefore, the blue, red, and green lights blink together every 60 seconds.

3. **Determine how many 60-second intervals occur in 30 minutes**:
   Half an hour is 30 minutes, which is:

   \[
   30 \times 60 = 1800 \text{ seconds}
   \]

   Now, divide 1800 seconds by the 60-second interval when all the lights blink together:

   \[
   \frac{1800}{60} = 30
   \]

Thus, the blue, red, and green neon lights will blink together **30 times** in half an hour.

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Do you want more details or have any questions?

Here are 5 related questions:
1. What is the LCM of 8, 12, and 16?
2. How many times will two lights blink together in 10 minutes if their intervals are 7 seconds and 9 seconds?
3. How do you calculate the greatest common divisor (GCD) of two numbers?
4. If the green light had a different interval, say 8 seconds, how would that affect the total?
5. Can the problem be extended to more than three lights with different intervals?

**Tip:** LCM is useful when dealing with repeating events to find when they will coincide.

Find out how many times a blue, red, and green neon light will blink together in 30 minutes. This math problem involves calculating the least common multiple (LCM) of the blinking intervals and applying basic time conversion. Suitable for students in Grades 6-8.

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