  ### Home > MC1 > Chapter 2 > Lesson 2.1.3 > Problem2-34

2-34.

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.

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

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 $4$ $8$ $12$

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?

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?

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.

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

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