Activities

1. What is the prime factorization of 120x²y³ ?

2. What is the greatest common factor of 400 and 560 ?

3. What is the least common multiple of 24 and 32 ?

4. What is the greatest common factor of 191a³b⁴c and 121a²c³ ?

5. What is the greatest common factor and least common multiple of m⁴n² and m³n?

6. What is the greatest common factor and least common multiple of 64p⁶q¹⁰r² and 30pq¹⁴r²² ?

7. Ingrid wants to buy the same amount of t-shirts as socks for her daughter Audrey. If t-shirts come in packs of 12 and socks come in packs of 10 what is the least amount of socks that Ingrid will have to buy?

8. The Broad Street subway line express train stops at city hall every 16 minutes. The local train stops at the station every 10 minutes. If you arrived at the station just as both trains left, how long will you have to wait until they both arrive at the same time again?

9. William is building a cutting board out of two types of wood, maple and walnut. The maple board is 80 inches long and the walnut board is 36 inches long. If William wants to cut all of his lumber into strips of equal width, what is the largest size strip he can create?

10. Find the LCM of the following three monomials:  21a²b, 32ab, and 45ab³.

11. Jared was asked to complete the following addition problem. What number should he use as a common denominator in order to add the fractions properly?

12. Pam, Jacob and Matt were each counting. Pam was counting by threes, Jacob was counting by fours and Matt was counting by fives. From 1-500 how many numbers did all three of them say?

13. Krista was attempting to factor the following polynomial:   -160x⁴y⁵ + 64x²y³ – 82x⁴y, what monomial should she factor out of the polynomial?

14. The greatest common factor of two monomials is 8pq². If one of the monomials is 56pq⁵r, what could the other monomial be?

15. If the least common multiple of four monomials is 180x²y³z⁴, what could the four monomials be?

16. Create three different monomials such that the greatest common factor of the three is 5x² and the least common multiple is 60x³y²z.

17. Assuming x is a positive integer, why does the LCM of x and x+1 equal x² + x?

18. Create a Venn diagram to show the GCF and LCM of 27x³y⁴ and 162xy⁵z.

Answer Key/Rubric

2. 80

3. 96

4. a²c

5. GCF: m³n, LCM: m⁴n²

6. GCF:  2pq¹⁰r², LCM: 960p⁶q¹⁴r²²

7. 60 socks

8. 80 minutes

9. 4 inches

10. 10,080a²b³

11. 420

12. 8

13. 4x²y

14. 40p³q²; Things to look for in the answer - 8 times any prime number except 7, must have 1 or more p's, exactly 2 q's, may have any other letter but r

15. Various answers including: 180, x², y³, z⁴; things to look for - none of the numbers/letters can exceed: two - 2's, two - 3's, one - 5, two - x's, three - y's, four - z's; at least one of the four answers must contain the max for each group

16. Various answers including: 5x², 15x²y², 20x³z; things to look for - Each answer must have exactly one factor of 5 and two x’s; At least one answer, but not more than two answers, must have two factors of 2, and one factor of 3, three factors of x, two factors of y, and one factor of z

17. The LCM of x and x+1 equals x² + x because any two consecutive integers do not share any prime factors.