Activities

1. Find the greatest common factor (GCF) of 48 and 30

2. Find the least common multiple (LCM) of 6 and 8.

3. Complete the Venn diagram below and list the common factors in order of least to greatest. 

4. The lunch menu at a local restaurant offers specials on certain days during the week.  Pizza is served every 4^th day and hotdogs are served every 3^rd day.  How many days will go by before pizza and hotdogs will be served on the same day?

5. A baker has 27 glazed doughnuts and 36 jelly filled doughnuts that are going to be divided into boxes.  Each box must have the same number of glazed and the same number of jelly filled doughnuts in it.  What is the greatest number of boxes that the baker can make using all of the doughnuts?

6. The 6^th grade class is having a school field day competition.  There are 40 girls and 32 boys who want to participate in the relay race.  Each relay team must have the same number of boys and girls on it.  What is the greatest number of teams that can be formed?  How many girls and boys would be on each team?  Explain.

7. You want to have an equal number of cups and plates at your party.  What is the fewest number of packs that you can buy of each item based on the chart below?  Explain how you found your answer.

8. You want to invite 60 people to a party.  Using the chart below, what is the least number of packs of invitations and plates that you can buy so that each person will get one and not have any left over? Explain how you found your answer.

Answer Key/Rubric

1. GCF = 6
   
   
2. LCM = 24

3. The common factors in order from least to greatest are 1, 2, 3, 6, 9, and 18.

   

4. Pizza and hotdogs will both be served on the 12^th day of the lunch special cycle.  The LCM of 3 and 4 is 12.

5. The greatest number of boxes that the baker can make with an equal number of each type of doughnut is 9 boxes. The GCF of 27 and 36.  There will be 3 glazed and 4 jelly in each.

6. 8 teams with 5 girls and 4 boys each.

Acceptable explanations might include, but are not limited to

• Listing out all the factors of both 40 and 32
• Finding that the GCF is 8
• Stating that 8 is the greatest number of teams that can be made with an equal amount of boys and girls on it
• Divide 40 girls by 8 teams to get 5 for each team 
• Divide 32 boys by 8 team to get 4 for each team

7. 3 packs of cups; 2 packs of plates

Acceptable explanations might include, but are not limited to

• Listing out the multiples of both 8 and 12
• Finding that the LCM is 24
• You have to buy 3 packs of cups
• You have to but 2 packs of plates

8. 5 packs of plates; 12 packs of invitations

Acceptable explanations might include, but are not limited to

• Listing the multiples of 5 and 12 until both of the lists contain 60
• Find the factors that are multiplied by 5 and 12 to equal 60
• You need to buy 5 packs of plates
• You need to buy 12 pack of the invitations