1. **State the problem:** Two neon lights blink periodically, one every 4 seconds and the other every 6 seconds. We want to find how many times they blink simultaneously in 60 seconds. 2. **Identify the key concept:** The lights blink together at times that are common multiples of their blinking intervals. 3. **Find the least common multiple (LCM):** The LCM of 4 and 6 gives the interval at which both blink together. 4. **Calculate the LCM:** - Prime factors of 4: $2^2$ - Prime factors of 6: $2 \times 3$ - LCM is the product of the highest powers of all primes: $2^2 \times 3 = 4 \times 3 = 12$ 5. **Determine the number of simultaneous blinks in 60 seconds:** - They blink together every 12 seconds. - Number of times they blink together in 60 seconds is $\frac{60}{12} = 5$ 6. **Include the initial time (0 seconds):** Since they start blinking at the same time (0 seconds), count this as the first blink. 7. **Final count:** The times are at 0, 12, 24, 36, 48, and 60 seconds, totaling 6 times. **Answer:** They blink together 6 times in 60 seconds.