GCF and LCM Challenges: Real-Life Problem Solving

1. Sarah has 24 apples and 36 oranges. What is the greatest common factor (GCF) of the number of apples and oranges she has?

• 12

• 6

• 18

• 24

2. A gardener is planting flowers in rows. If he has 18 red flowers and 24 yellow flowers, what is the least common multiple (LCM) of the number of red and yellow flowers he can plant in each row?

• 72

• 48

• 36

• 60

3. Two friends are making gift bags. One has 15 candies and the other has 25 candies. What is the greatest number of identical gift bags they can make without any candies left over?

• 20

• 10

• 3

• 5

4. A teacher has 30 pencils and 45 erasers. What is the greatest common factor (GCF) of the number of pencils and erasers?

• 25

• 15

• 20

• 10

5. A baker is making cookies and brownies. If he can make 12 cookies in an hour and 15 brownies in an hour, how long will it take him to make the same number of cookies and brownies?

• 12 hours

• 3 hours

• 6 hours

• 9 hours

6. Emily is organizing her book collection. She has 40 fiction books and 60 non-fiction books. What is the greatest common factor (GCF) of the number of fiction and non-fiction books?

• 50

• 30

• 10

• 20

7. A music teacher has 28 music sheets and 42 practice sheets. What is the least common multiple (LCM) of the number of music sheets and practice sheets he can distribute evenly to his students?

• 84

• 96

• 72

• 56

8. Two cyclists are riding at different speeds. One completes a lap every 12 minutes and the other every 18 minutes. How often will they meet at the starting point?

• 36 minutes

• 24 minutes

• 30 minutes

• 48 minutes

9. A factory produces 36 toys and 48 games. What is the greatest common factor (GCF) of the number of toys and games produced?

• 6

• 18

• 24

• 12

10. A group of friends is sharing 20 cupcakes and 30 cookies. What is the greatest number of equal portions they can create without any leftovers?

• 5

• 15

• 10

• 25