Some cicadas, comonly called 13 locust come above ground every 13 years, while others called 17 years locusts,

Question

Stephan conjectured that both 13-year and 17-year locusts came out that year. Assume Stephan's conjecture is correct. How many years will pass between the years when both 13-year and 17 locusts are out at the same time?

Stephan's grandfatherbtold him about a terrible year when the cicadas were so numerous that they ate all the crops on his farm. Stephan conjectured that both 13-year and 17-year locusts came out that year. Assume Stephan's conjecture is correct. How many years will pass between the years when both 13-year and 17 locusts are out at the same time?

Answer 1

The least common multiple is just 13*17 = 221, since the two numbers are both prime.

So it will be 221 years until the 13-year and 17-year cycles match up again.