George gets his hair cut every 4 weeks and Veronica gets hers cut every 6 weeks. When will they next have haircuts the same week?

Question

may need to use prime numbers in the answer.

 

Answer 1

The LCM (Least Common Multiple) is easily found in two ways:

 

1. List the multiples and find the first value in both lists.

    Multiples of 4:    4   8   12   16   20   24   28   32

    Multiples of 3:    3   6   9   12   15   18   21   24   27

  Note that 12 is the first number that appears in both lists.  Thereafter, multiples of 12 appear in both lists.

 

2.  Determine the number that has all the prime factors of the values:

   Prime factors of 4:    2   2

   Prime factors of 3:     3

 Number that includes the prime factors (without including twice) of the values:   2*2*3 = 12

  The LCM is 12.

 

If George and Veronica both get their hair cut this week (t=0), then the next time that they both get their hair cut is in week 12 (t=12).