Janet practices every other dayand Sally practices every 5 days. the meet one day. How many days will it take before they meet again?

Question

Janet and Sally are friends who are on different soccer teams.  They practice at the same field.  Janet practices every other day and Sally practices every 5 days.  The meet on the field one day.  How many days will it take before they meet again>

Answer 1

This is a lot like finding a common denominator when adding fractions.

Janet will be at the practice field 2, 4, 6, ... days later.  These are the multiples of 2.

Sally will be there again in multiples of 5 days.

5, 10, 15, ...

Find the lowest common multiple of 2 and 5.

 

Start by examining the multiples of the larger number until you find the first one that is also a multiple of 2.

5 is not a multiple of 2.

10 is a multiple of 2.

 

The answer is 10.

 

(You could start with the smaller number and get the same result.  It just takes longer.)

2 is not a multiple of 5.

4 is not a multiple of 5.

6 is not a multiple of 5.

8 is not a multiple of 5.

10 is a multiple of 5