### Home > MC1 > Chapter 1 > Lesson 1.2.4 > Problem1-95

1-95.

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

 Two Three $2$ $4$ $6$ $3$ $6$

Remember, counting by $2$'s means that you should add $2$ to each number to get the next number. For example, you can see that the first number in the sequence is two and the next number is $4$. Adding $2$ to $4$, the next number is $6$. ($2+2=4$ and $4+2=6$)

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

$6$, $12$, and $18$ are in both rows.

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

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

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

3. In the table, what is the greatest common multiple of both two and three?

Remember, the greatest common multiple is the largest multiple two factors have in common. Refer to part (a) again.

4. Write three more common multiples of two and three.

To answer this question, it will help to keep counting by $2$'s and $3$'s.

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