Copy and complete the table of multiples below (count by $3$'s and count by $4$'s). Extend the table so that it has $14$ columns of values.

1. Write down all the numbers that appear in both the $3$'s row and the $4$'s row. Describe any pattern that you notice.

   Hint (a):

   If you are having trouble filling out the table, it may be helpful to refer to your Multiplication Table. Also, you can simply add 3 or 4 to each previous value to produce a new multiple.

   Three	$3$	$6$	$9$	$12$
   Four	$4$	$8$	$12$

   Answer (a):

   The table is filled out below. Do you see any patterns? Perhaps there are several multiples of another number? Don't forget to describe the patterns you notice.
   

   Three

   $3$

   $6$

   $9$

   $12$

   $\color{red}{15}$

   $\color{red}{18}$

   $\color{red}{21}$

   $\color{red}{24}$

   $\color{red}{27}$

   $\color{red}{30}$

   $\color{red}{33}$

   $\color{red}{36}$

   $\color{red}{39}$

   Four

   $4$

   $8$

   $12$

   $\color{red}{16}$

   $\color{red}{20}$

   $\color{red}{24}$

   $\color{red}{28}$

   $\color{red}{32}$

   $\color{red}{36}$

   $\color{red}{40}$

   $\color{red}{44}$

   $\color{red}{48}$

   $\color{red}{52}$

2. What is the smallest multiple of both three and four?

   Hint (b):

   Here, you should look for the least common multiple. Remember, the least common multiple is the smallest number that $3$ and $4$ share as multiples, or have in common.

3. From your list, what is the largest multiple of both three and four?

   Hint (c):

   Look at the chart above and find the largest number that appears in both rows.

4. Write three more numbers that are multiples of both three and four.

   Hint (d):

   It will help to extend your chart to find the next multiples.

   Answer (d):

   The next three common multiples in the sequence are $48,60,$ and $72$.