  ### Home > CC1 > Chapter 2 > Lesson 2.3.2 > Problem2-66

2-66.

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 rows. Describe any pattern(s) 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.

$\left. \begin{array} { | c | c | c | c | c | c | c | c | c | c | c | } \hline \; \; \text{Three}\; \; & { 3 } & { 6 } & { 9 } & { 12 } & { \color{red}{15} } & { \color{red}{18} } & { \color{red}{21} } & { \color{red}{24} } & { \color{red}{27} } & { \color{red}{30} } & { \color{red}{33} } & { \color{red}{36} } & { \color{red}{39} } \\ \hline \text{Four} & { 4 } & { 8 } & { 12 } & { \color{red}{16} } & { \color{red}{20} } & { \color{red}{24} } & { \color{red}{28} } & { \color{red}{32} } & { \color{red}{36} } & { \color{red}{40} } & { \color{red}{44} } & { \color{red}{48} } & { \color{red}{52} } \\ \hline \end{array} \right.$

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

2. What is the smallest multiple of both $3$ and $4$?

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. Write three more numbers that are multiples of both $3$ and $4$.

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

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