1. LCM & GCF Unit Quiz – Factors & Multiples January 5th
MAKE CORRECTIONS, COMPLETE NB, AND UPDATE GLOSSARY

2. Write the correct word or words to complete each sentence.
A number multiplied by another number is a ________.
48 is a ___________ of 12.
The same number in two lists is called a ____________ number.
The ____________________ of 90 and 72 is 18.
The ____________________ of 6 and 9 is 18.

3. Write the correct word or words to complete each sentence.
A number multiplied by another number is a _factor__.
48 is a __multiple__ of 12.
The same number in two lists is called a ___common___ number.
The _greatest common factor_ of 90 and 72 is 18.
The _least common multiple _ of 6 and 9 is 18.

4. Question 1 Starting at 8.30am, tours of the National Capitol and the White House begin at a tour agency. Tours for the National Capitol leave every 15 minutes. Tours for the White House leave every 20 minutes. How often do the tours leave at the same time?

5. Question 1 Think: Find the lowest common multiple of 15 and 20.
This is how often the tours leave at the same time.
Solve:
15: 15, 30, 45, 60…
20: 20, 40, 60…
Answer:
Tours leave at the same time every 60 minutes.

6. Question 2 Two lights are turned on at the same time
Question 2 Two lights are turned on at the same time. One blinks every 4 seconds and the other blinks every 6 seconds. In 60 seconds, how many times will they blink at the same time?

7. Question 2 Think: Find the lowest common multiple of 4 and 6.
This is how often the lights blink at the same time.
Divide 60 seconds by the LCM to find how many times they blink together in 60 seconds.
Solve:
4: 4, 8, 12, 16, 20, 24…
6: 6, 12, 18, 24…
60/12 = 5
Answer:
The lights blink at the same time 5 times in 60 seconds.

8. Question 3 The Ching Shin choir teacher plans to arrange the students in equal rows. Only boys or girls will be in each row. What is the greatest number of students that could be in each row?
Students
Number
Girls 48
Boys 64

9. Question 3 Think: Find the greatest common factor of 48 and 64.
This is the greatest number of students that could be in each row.
Solve:
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
64: 1, 2, 4, 8, 16, 32, 64
Answer:
There could be 16 students in each row.

10. Question 4 Rafaela is a physical education teacher and has 25 girls and 35 boys in her class. She wants to divide the class into teams of the same size, where each team has the same number of girls and the same number of boys. If Rafaela creates the greatest number of teams possible, how many boys will be on each team?

11. Question 4 Think Find the GCF of 25 and 35
Question 4 Think Find the GCF of 25 and 35. This is the greatest number of teams that Rafaela can make. To find the number of boys on each team, divide the number of boys by the number of teams. Solve 25: 1, 5, 25 35: 1, 5, 7, 35 35/5 = 7 Answer There will be 7 boys on each team.

12. Question 5 Tim has 39 pairs of headphones and 13 music players
Question 5 Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all of the headphones and music players in identical packages. What is the greatest number of packages Tim can make?

13. Question 5 Think Find the greatest common factor of 39 and 13
Question 5 Think Find the greatest common factor of 39 and 13. Solve 39: 1, 3, 13, 39 13: 1, 13 Answer The greatest number of identical packages that Tim can make is 13.

14. Question 6 William and Luis are in different physics classes at Santa Rita. Luis’s teacher always gives exams with 30 questions on them, while William’s teacher gives more frequent exams with only 24 questions. Even though the two classes have to take a different number of exams, their teachers have told them that both classes will get the same total number of exam questions each year. What is the minimum number of exam questions that the students in both classes can expect to take in a year?

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Question 6 Think Find the lowest common multiple of 30 and 24. Solve 30: 30, 60, 90, 120, 150… 24: 24, 48, 72, 96, 120, 144… Answer The minimum number of exam questions that the students in both classes can expect to take in a year is 120.

16. Question 7 Sam and Carlos are bowling with plastic pins in Sam's living room. Remarkably, Sam knocks down 8 pins on every bowl, and Carlos knocks down 9 pins on every bowl. At the end of the day, Sam and Carlos have knocked down the same total number of pins. What is the least number of total pins that Sam and Carlos could have each knocked down?

17. Question 7 Think Find the lowest common multiple of 8 and 9
Question 7 Think Find the lowest common multiple of 8 and 9. Solve 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80… 9: 9, 18, 27, 36, 45, 54, 63, 72, 81… Answer The least number of pins that they could have each knocked down is 72.

18. Question 8 There are 32 forwards and 80 guards in Leo's basketball league. Leo must include all players on a team and wants each team to have the same number of forwards and the same number of guards. If Leo creates the greatest number of teams possible, how many guards will be on each team?

19. Question 8 Think Find the greatest common factor of 32 and 80
Question 8 Think Find the greatest common factor of 32 and 80. This is the number of teams. Divide the number of guards in the league by the number of teams. Solve 32: 1, 2, 4, 8, 16, 32 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 80/16 = 5 Answer There will be 5 guards on each team.