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