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LCM and GCF Quiz

Total questions: 55

Worksheet time: 48mins

Name
Class
Date
1.

Carleigh is preparing identical breakfast gift sets. There are 18 boxes of pancake mix and 27 jars of jam. What is the greatest number of gift sets she can prepare using all of the pancake mix and jam?

a)

485

b)

3

c)

9

d)

12

2.

Josh and Eva are packing first-aid supplies. It takes Josh 12 minutes to fill a box with bandages. It takes Eva 8 minutes to fill a box with antibiotics. If they start packing boxes at the same time, how long will it be before they start filling a new box at the same time?

a)

24

b)

9

c)

96

d)

36

3.

Sadie is helping her mother stain some shelves. Sadie stains a shelf every 25 minutes. Her mother stains a shelf every 15 minutes. If they start together, how long will it be before they finish staining a shelf at the same time?

a)

5

b)

50

c)

3

d)

25

4.

A jeweler is making identical necklaces. He has 24 gold beads and 144 colored glass beads. What is the greatest number of necklaces he can make using all the gold beads and glass beads?

a)

3456

b)

12

c)

2

d)

4

5.

What is the greatest common factor of the following numbers:

18 and 81

a)

3

b)

2

c)

9

d)

18

6.

What is the greatest common factor of the following numbers:

14, 42, and 49

a)

3

b)

7

c)

2

d)

84

7.

What is the least common multiple of the following numbers:

9 and 12

a)

24

b)

3

c)

18

d)

36

8.

What is the least common multiple of the following numbers:

3, 7, and 21

a)

1

b)

3

c)

21

d)

42

9.

Taylor is making identical balloon arrangements for the homecoming dance. She has 12 red balloons, 24 green balloons, and 18 blue balloons. What is the greatest number of arrangements that she can make?

a)

6

b)

9

c)

2

d)

3

10.

Train "A" leaves a subway station every 12 minutes. Train "E" leaves every 9 minutes. If both trains just left the station on parallel tracks, when will both leave the stations together again?

a)

108 minutes

b)

3 minutes

c)

36 Minutes

d)

45 minutes

11.

A video game has 3 villains who appear on screen at different intervals. One villain appears every 5 seconds, a second villain appears every 10 seconds, and a third villain appears every 16 seconds. how much time passes between occasions when all three villains appear at the same time?

a)

32 seconds

b)

80 seconds

c)

125 seconds

d)

60 seconds

12.

Pencils come in packages of 10. Erasers come in packages of 12. Dean wants to purchase the smallest number of pencils and erasers so that he will have exactly 1 eraser per pencil. How many packages of pencils and erasers should Dean buy?

a)

5 packages of pencils and 4 packages of erasers.

b)

4 packages of pencils and 3 packages of erasers.

c)

6 packages of pencils and 5 packages of erasers.

d)

12 packages of pencils and 10 packages of erasers.

13.

Ms. Corvino has 84 packs of pretzels and 56 juice boxes. She wants to share them equally with the in-person 6th graders with nothing leftover. What is the greatest number of students that can receive pretzels and juice boxes?

a)

4

b)

14

c)

7

d)

28

14.

Plastic forks come in packs of 8, spoons in packs of 10, and knives in packs of 12. What is the smallest number of forks, knives and spoons that you could have to have the same number each?

a)

24

b)

120

c)

60

d)

40

15.

Nancy practices her tiktok dances often. She practices the #shotxcrisis dance every 4 days, #positions dance every 6 days, and #franchise dance every 9 days. If she practices all three of them today, how many days will it be until she practices all 3 dances on the same day again?

a)

36 days

b)

18 days

c)

24 days

d)

72 days

16.

Mrs. Greenberg, the 7th grade math teacher, has 15 logic puzzles, 10 visual puzzles and 30 word puzzles that she wants to group into sets for students who finish their tests early. Mrs. Greenberg wants each set to be identical, containing the same combination of logic puzzles and visual puzzles, with no puzzles left over. What is the most number of sets she can create?

a)

5 sets

b)

15 sets

c)

30 sets

d)

55 sets

17.

Is this an least common multiple problem, greatest common factor problem, or neither?

Andy is planning a birthday party. His mom said she would make 18 personal pizzas and 27 mini-cupcakes. How many people can Andy invite to his party so the pizza and cupcakes are shared equally among his friends with nothing leftover? How many pizzas and cupcakes will each person get?

a)

Least Common Multiple

b)

Greatest Common Factor

c)

Neither

18.

Is this a least common multiple problem, greatest common factor problem, or neither?

Mr. Bluestone purchased boxes of baseballs contains 15 balls each and boxes of gloves each containing 25 gloves. Mr. Bluestone purchased the same number of balls and gloves. How many balls and gloves he did purchase if he bought the same number of each?

a)

LCM

b)

GCF

c)

Neither

19.

What is the GCF of 99 and 45?

a)

18

b)

3

c)

9

d)

11

20.

What is the GCF of 20, 40 and 72?

a)

8

b)

4

c)

360

d)

2

21.

What is the greatest common factor of 39 and 13?

a)

3

b)

13

c)

1

d)

39

22.

What is the least common multiple of 15 and 9?

a)

90

b)

3

c)

45

d)

135

23.

Two buses leave the station at 6:00am. Bus A has a long route and leaves the station every 75 minutes.

Bus B has a short route and leaves the station every 15 minutes.


What is the next time Bus A and Bus B will leave the bus station at the same time?

a)

Least Common Multiple/LCM like the hot dog problem

b)

Greatest Common Factor/GCF like the valentine problems

c)

Neither

24.

Adali has two electric train sets: A and B. Each train is on its own circular track. She starts both trains at the same time. Train A returns to its starting point every 12 seconds. Train B returns to its starting point every 9 seconds. If the trains continue traveling, what is the least amount of time, in seconds, that both trains will arrive at the starting points at the same time?

a)

Least Common Multiple/LCM like the hot dog problem

b)

Greatest Common Factor/GCF like the valentine problem

c)

Neither

25.

Jerennys and her crew have 90 Jolly Ranchers and 36 Hershey Kisses. They want to create goodie bags to give to essential workers in the neighborhood to thank them for their sacrifice during the pandemic.


They want to create as many goodie bags that are exactly the same without having anything leftover. How many goodie bags can they make?

a)

Least Common Multiple/LCM like the hot dog problem

b)

Greatest Common Factor/GCF like the valentine problem

c)

Neither

26.

On Saturday, a minor league baseball team gave away baseball cards to each person entering the stadium. One group received 28 baseball cards. A second group received 68 baseball cards. If each person entering the stadium received the same number of cards, what was the greatest possible number of baseball cards that each person could have received?

a)

Least Common Multiple/LCM like the hot dog problem

b)

Greatest Common Factor/GCF like the valentine problem

c)

Neither

27.

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?

a)

Least Common Multiple/LCM like the hot dog problem

b)

Greatest Common Factor/GCF like the valentine problem

c)

Neither

28.

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 kids will be on each team?

a)

Least Common Multiple/LCM like the hot dog problem

b)

Greatest Common Factor/GCF like the valentine problem

c)

Neither

29.

Wesley goes to the park every 6th day. Andy goes to the same park every 7th day. How many times will they meet in the park in the month of December and January if we start counting from December 1st?

a)

Least Common Multiple/LCM like the hot dog problem

b)

Greatest Common Factor/GCF like the valentine problem

c)

Neither

30.

I want to plant 45 sunflower plants, 81 corn plants and 63 tomato plants in my garden. If I put the same number of plants in each row and each row has only one type of plant, what is the greatest number of plants I can put in one row?

a)

Least Common Multiple/LCM like the hot dog problem

b)

Greatest Common Factor/GCF like the valentine problem

c)

Neither

31.

What is the greatest common factor of 15 and 18?

a)

33

b)

1

c)

3

d)

5

32.

Select all the numbers that are common factors of 24 and 30?

a)

3

b)

6

c)

2

d)

12

e)

8

33.

What is the least common multiple of 4 and 12?

a)

48

b)

16

c)

12

d)

4

34.

What is the LCM of 15 and 20?

a)

300

b)

5

c)

120

d)

60

35.

What is the least common multiple of 4, 6, and 10?

a)

20

b)

60

c)

24

d)

40

36.

What is the LCM of 12 and 14?

a)

84

b)

168

c)

2

d)

26

37.

What is the least common multiple of 3, 4 and 8?

a)

12

b)

48

c)

1

d)

24

38.

What's the LCM of 5 and 15?

a)

5

b)

75

c)

30

d)

15

39.

What is the least common multiple of 2, 5, and 10?

a)

1

b)

5

c)

10

d)

30

40.

What is the least common multiple of 6 and 7?

a)

21

b)

1

c)

42

d)

28

41.

What is the LCM of 3 and 13?

a)

1

b)

3

c)

39

d)

78

42.
You have 18 red legos and 24 green legos.  You need to combine them into groups of the same size with the same number of red and green legos in each group.
A.  What is the greatest number of groups you can make?
B.  How many red and green legos will be in each group?
a)
A.  6 groups  B.  3 red and 4 green
b)
A.  72 groups  B.  6 red and 3 green
c)
A.  3 groups  B.  6 red and 8 green
43.
You have a set of 12 hearts, 16 diamonds, and 20 clubs that need to be put into equal groups.  Each group must be made up of the same number of hearts, diamonds, and clubs.  What is the greatest number of groups that can be made?
a)
6 groups
b)
2 groups
c)
4 groups
44.
You are watching a parade and observe cars going by in groups of 4 blue cars and 6 green cars at a time.  If you observe the same number of blue and green cars, what is the smallest number of each car you could have observed?
a)
2 cars
b)
12 cars
c)
24 cars
45.
Sara had 16 red flowers and 24 yellow flowers.  She wants to make bouquets with the same number of each color flower in each bouquet.  What is the greatest number of bouquets that she can make?
a)
4
b)
2
c)
48
d)
8
46.
Two clocks are turned on at the same time. One clock chimes every 15 minutes. The other clock chimes every 25 minutes. In how many minutes will they chime together?
a)
55 minutes
b)
25 minutes
c)
60 minutes
d)
75 minutes
47.
Lisa is making activity baskets to donate to charity.  She has 12 coloring books and 36 crayons.  What is the greatest number of baskets she can make if each type of toy is equally distributed among the baskets?
a)
2
b)
12
c)
36
d)
6
48.
At the movie theater, they give out a free drink to every 75th customer and a free bag of popcorn to every 30th customer. Who is the first customer that is going to win both free items?
a)
16th customer
b)
150th customer
c)
300th customer
d)
180th customer
49.

What is the GCF (Greatest Common Factor) of 12 and 6?

a)

1

b)

6

c)

2

d)

3

50.

What is the LCM (Least Common Multiple) of 4 and 10?

a)

4

b)

40

c)

15

d)

20

51.

Find the GCF (Greatest Common Factor) of 50 and 40.

a)

5

b)

2

c)

10

d)

8

52.

What is the GCF (Greatest Common Factor) of 12 and 30?

a)

4

b)

2

c)

5

d)

6

53.

Find the LCM (Least Common Multiple) of 18 and 24.

a)

6

b)

72

c)

24

d)

5

54.

What is the LCM (Least Common Multiple) of 8 and 5?

a)

50

b)

40

c)

5

d)

8

55.

What is the GCF (Greatest Common Factor) of 25 and 15?

a)

5

b)

10

c)

15

d)

20

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