Chapter CSB1.3, Problem 26E

To determine

The next year in which cicadas and tent caterpillars will coincide.

Answer to Problem 26E

2100

Explanation of Solution

Given information:

Life cycle of Cicada is 17 yr. and that of Tent Caterpillar is 6 years.

Calculation:

Number of years after which Cicadas and tent caterpillars coincide is equal to LCM of 17 and 6.

Prime factors of 17 and 6 are as follows:

  $\begin{array}{l}17={17}^1\\ 6=2^1\times 3^1\end{array}$

Therefore LCM = ${17}^1\times 2^1\times 3^1=102$ .

Hence Cicadas and tent caterpillars will coincide again after 102 years from 1998. Thus they will coincide in year 2100.