Copy and complete the table of multiples below. (Count by $2$’s and count by $3$’s).

1. Write down all the numbers that appear in both rows.  Describe any pattern(s) that you notice. 

   Partial Answer (a):

   $6, 12, \text{and } 18$ are in both rows.

   Hint (a):

   What do you notice about these numbers? Are they multiples of a number other than $2 \text{ and } 3$?

2. What is the smallest number that appears in both rows?  This number is said to be the least common multiple of $2$ and $3$. 

   Hint (b):

   Looking at part (a) of this problem may make this easier.

3. Find three more common multiples of $2$ and $3$.

   Hint (c):

   Keep counting by $2$'s and $3$'s.

   Answer (c):

   Three more common multiples of $2$ and $3$ are $24$, $30$, and $36$.

4. Can you find the largest number that is a common multiple of both $2$ and $3$? If so, what is it? If not, explain why not.

   Hint (d):

   The largest common multiple would be the greatest number that is a multiple of both of the two factors. Refer to part (a) again.