CPM Homework Help : CC1MN Problem 1-88

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

Two

Two, column 1 $2$

Two, column 2 $4$

Two, column 3 $6$

Two, column 4, blank

Two, column 5, blank

Two, column 6, blank

Two, column 7, blank

Two, column 8, blank

Two, column 9, blank

Three

Three, column 1 $3$

Three, column 2 $6$

Three, column 3, blank

Three, column 4, blank

Three, column 5, blank

Three, column 6, blank

Three, column 7, blank

Three, column 8, blank

Three, column 9, blank

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 $2 \text{ and } 3$ ?
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.
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 $36$ .
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.