Some cicadas called 13 year locusts come above ground every 13 years, while others called 17 year locusts come out every 17 years. Mark's grandmother told him about a terrible year when then cicadas were so numerous that they ate all the crops on her farm. Mark thought that both 13 year and 17 year locusts came out that year. Assume Mark thought is correct. How many years will pass between the years when both 13 year and 17 year locusts are out at the same time?

Question

Some cicadas called 13 year locusts come above ground every 13 years, while others called 17 year locusts come out every 17 years. Mark's grandmother told him about a terrible year when then cicadas were so numerous that they ate all the crops on her farm. Mark thought that both 13 year and 17 year locusts came out that year. Assume Mark thought is correct. How many years will pass between the years when both 13 year and 17 year locusts are out at the same time?

Answer 1

To find the next occurrence of extreme famine, we need to find the least common multiple (LCM) of the two recurrence intervals of 13 and 17.

LCM has the property that if the numbers are both prime, LCM is the product of the two numbers.

Since 13 and 17 are both prime, the LCM equals 13*17 = 221.

So it will be 221 years before the locusts come out again in the same year, assuming they are forever regular!