Question 1: Suppose a ghost floats by every two weeks and a skeleton rattles along every three days, a pumpkin rolls by every 6 days. If a ghost floated by, a skeleton rattled along and a pumpkin rolled by today, how long would it be before you see all three again on the same day?
Question 2: There just so happened to be a bat flying with the group today. The next time you see all four again is in 84 days. How often do the bats fly by?
Answers (2)
Q1. You want the lowest common multiple of 14, 3 and 6
= 42 days
Q2. 4 days
(could also be every 12 days or every 28 days or even every 84 days!
Split 84 days down into prime factors
2 x 2 x 3 x 7
2 squared doesn't feature in the prime factors of 3, 6 or 14, but all the other factors (3 & 7) do. Therefore the number of days that bats fly down MUST be a multiple of 4. Its other factors can only be 3 or 7.
therefore it can be
a) 4
b) 4 x 3 = 12
c) 4 x 7 = 28
d) 4 x 3 x 7 = 84
Q1. 42 days
Q2. Every 12 days