a manager turns on the restaurants two neon signs at the same time. both signs blink as they are turned on. one sign blinks every 20 seconds and the other blinks every 15 seconds. in how many seconds will they blink together again?

What is the least common multiple of 20 and 15?

20 + 15 =35

To determine when the two neon signs will blink together again, we need to find the least common multiple (LCM) of their times. The LCM is the smallest multiple that both numbers share.

Let's find the LCM of 20 seconds and 15 seconds using the prime factorization method:

Prime factorization of 20: 2 * 2 * 5 = 2^2 * 5
Prime factorization of 15: 3 * 5

We take the highest exponent for each prime factor:
2^2 * 3 * 5 = 60

Therefore, the two neon signs will blink together again after 60 seconds.