Dave passes every 8 minutes, and Geoff passes every 15 minutes.

What do we need to find: How long will it take them to meet again?

What should we do: We need to find the least common multiple (LCM) of both of their times, so we can find the earliest point where they met each other again.

**But what is the LCM?**

The Least Common Multiple (LCM) is also referred to as the Lowest Common Multiple (LCM) and Least Common Divisor (LCD). For two integers a and b, denoted LCM(a,b), **the LCM is the smallest positive integer that is evenly divisible by both a and b.** For example, LCM(2,3) = 6 and LCM(6,10) = 30.

The LCM of two or more numbers is the smallest number evenly divisible by all numbers in the set.

As we are not allowed to use a calculator during the exam, we can solve the question by listing multiples or by prime factorization, *if you aren’t familiar with these methods, please navigate to our Appendix.*

To solve this question, I will use both methods as an example.

The easier one would be to list the multiples, it will allow you to find and recognize the answer using visual elements:

Dave: 8,16,24,32,40,48,56,64,72,80,88,96,104,112,(120)

Geoff: 15,30,45,60,75,90,105,(120)

\frac{120}{60} = 2\ hours

Using the quicker method, we can use prime factorization and find the LCM:

LCM(8,15):

8=2x2x2

15=3x5

LCM: 2x2x2x3x5 = \frac{120}{60} = 2\ hours