The 17-year locust (Magicicada) can only be seen every 17 years. The 13-year locust only appears every 13 years. If they were both seen in the year 2019, in which year would they next both appear together?
Answer: They will next both appear together in the year 2240.
Step-by-step solution
Step 1: Identify the mathematical model
The 17-year locust appears in multiples of 17 years, and the 13-year locust appears in multiples of 13 years. To find when they will both appear together again, we must determine the lowest common multiple, or , of 17 and 13.
Step 2: Calculate the LCM of the two prime periods
Since 17 and 13 are both prime numbers, their only common factor is 1. Therefore, their lowest common multiple is simply the product of the two numbers, which is years.
Step 3: Determine the next year of co-emergence
Both species last appeared together in the year 2019. Adding the 221-year interval to 2019 gives .