### Using GCF and LCM to solve problems

```Using GCF and LCM to
solve problems
* Always use the SOLVE method*

1) Ana's Linens sells hand towels in sets of 4
and bath towels in sets of 8. If the store sold
the same number of each this morning, what
is the smallest number of each type of towel
that the store must have sold?

2) Charles has just moved to a new town
and wants to share plates of baked goods
with his neighbors. He has 20 cookies and
15 brownies to share, and wants to split
them equally among the plates with no
food left over. What is the greatest
number of plates he can make to share?

3) Sapphire and Jeanette are each assigned a
paper for a class they share. Sapphire
decides to write 11 pages at a time while
Jeanette decides to write 5 pages at a time.
If they end up writing the same number of
pages, what is the smallest number of pages
that the papers could have had?

4) In preparation for a conference, Miles is
setting up some stations where people can
create their own name tags. He has 15 name
tags and 6 pens, which he wants to distribute
evenly among the name tag stations with
none left over. What is the greatest number
of name tag stations that Miles can set up?

5) A club has 9 girls and 18 boys as
members. The president wants to break the
club into groups, with each group containing
the same combination of girls and boys. The
president also wants to make sure that no
one is left out. What is the greatest number
of groups the president can make?


1) The correct answer is 8
◦ You need to find the smallest number that is a multiple of
both 4 and 8. This is the least common multiple.
List the multiples of each number. Find the lowest number
that appears in both lists.
Multiples of 4: 4, 8, 12, 16, 20
Multiples of 8: 8, 16, 24, 32, 40
The least common multiple of 4 and 8 is 8. That means that
the minimum number of each type of towel that the store
must have sold is 8, because 2 sets of 4 hand towels is a
total of 8 hand towels and 1 set of 8 bath towels is a total of
8 bath towels.
The smallest number of each type of towel is 8.



2) The correct answer is 5
List the factors of each number. Find the largest
number that appears in both lists.
Factors of 20: 20, 10, 5, 4, 2, 1 Factors of
15: 15, 5, 3, 1
The greatest common factor of 20 and 15 is 5.
That means that the greatest possible number of
plates is 5, because 20 cookies could be put onto
5 plates with 4 cookies each and 15 brownies
could be put onto 5 plates with 3 brownies each.
The greatest number of plates Charles can make
is 5.


3) The correct answer is 55

You need to find the smallest number that is a multiple of
both 11 and 5. This is the least common multiple.
List the multiples of each number. Find the lowest number
that appears in both lists.
Multiples of 11: 11, 22, 33, 44, 55
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
The least common multiple of 11 and 5 is 55. That means
that the smallest number of pages is 55, because 5 sets of
11 pages written by Sapphire is 55 pages in total and 11
sets of 5 pages written by Jeanette is 55 pages in total.
The smallest number of pages the papers could have had
55.


4) The correct answer is 3

List the factors of each number. Find the
largest number that appears in both lists.
Factors of 15: 15, 5, 3, 1 Factors of 6: 6, 3,
2, 1
The greatest common factor of 15 and 6 is 3.
That means that the greatest possible
number of name tag stations is 3, because
15 name tags could be put at 3 stations with
5 name tags each and 6 pens could be put at
3 stations with 2 pens each.
The greatest number of name tag stations
Miles can set up is 3.


5) The correct answer is 9

List the factors of each number. Find the
largest number that appears in both lists.
Factors of 9: 9, 3, 1 Factors of 18: 18, 9, 6,
3, 2, 1
The greatest common factor of 9 and 18 is 9.
That means that the greatest possible
number of groups is 9, because 9 girls could
be split into 9 groups with 1 girl each and 18
boys could be split into 9 groups with 2 boys
each.
The greatest number of groups the president
can make is 9.
```