Plastic Baseball Bats

1
Plastic Baseball Bats

• Plastic baseball bats are sold in packs of 4, and
  plastic baseballs are sold in packs of 8. a coach
  wants to give each of his players one bat and one
  baseball. What is the LEAST number of packs of
  bats and balls he should buy so there are no bats
  and balls left over?

2
Answer

• 2 packs of bats
• 1 pack of baseballs
• Because the Least Common Multiple (LCM) of 4 and
  8 is 8. You need 2 packs of bats to get 8 total
  bats and 1 pack of baseballs to get 8 baseballs.

3
Pens and Pencils

• There are 42 pens and 63 pencils. All of the pens
  and pencils are given to the students in Mrs.
  Burchettes class. Each student receives the same
  number of pens and and the same number of
  pencils. What is the GREATEST number of students
  in the class?

4
Answer

• 21 Students
• Because the Greatest Common Factor (GCF) of 42
  and 63 is 21.

5
Fruit

• Mr. Limpert, a farmer, has 160 apples, 80 plums,
  and 120 pears. He wants to divide the fruit into
  packages with the same number of apples, the same
  number of plums, and the same number of pears in
  each package. What is the GREATEST number of
  packages he can have if every piece of fruit is
  placed in a package?

6
Answer

• 40 Packages
• Because the GCF of 160, 80, and 120 is 40.

7
Football

• In a football game, the Mustangs scored all
  touchdowns, which are worth 7 points. The Hoyas
  scored all the field goals, which are worth 3
  points each. Neither team went scoreless. The
  final score of the game was the LOWEST tie
  possible given these conditions. How many points
  did each team score?

8
Answer

• 21 Points
• Because the LCM of 7 and 3 is 21.

9
Dog Treats

• Dog treats come in packages of 6, and bones come
  in bags of 9. What is the LEAST number of treat
  boxes you could make so each dog has a treat box
  with one bone and one treat, and there are no
  bones or treats left over?

10
Answer

• 18 Treat Boxes
• Because the LCM of 6 and 9 is 18.

11
Olympic Tug-of-War

• There are 40 boys and 32 girls who want to
  participate in the tug-of-war at the Olympics. If
  each team must have the same number of girls and
  boys, what is the GREATEST number of teams that
  can race?

12
Answer

• 8 Teams
• Because the GCF of 40 and 32 is 8.

13
Coins

• Jonathan has 15 quarters, 30 dimes, and 48
  nickels. He wants to group his money so that each
  group has the same number of each coin. What is
  the GREATEST number of groups he can make?

14
Answer

• 3 Groups of Coins
• Because the GCF of 15, 30, and 48 is 3.

15
Party bags

• Anna wants to make party bags. Glitter pens come
  in packs of 6. Stickers come in sheets of 4, and
  bouncy balls come in packs of 3. What is the
  LEAST number of party bags she could make to have
  1 of each item in every party bag, and no
  supplies left over?

16
Answer

• 12 Party Bags
• Because the LCM of 6, 4, and 3 is 12.

17
Observations

• Notice for all of the questions that asked What
  is the GREATEST.., you found the Greatest
  Common Factor of the given numbers to solve the
  problem.
• Notice for all of the questions that asked What
  is the LEAST.., you found the Least Common
  Multiple of the given numbers to solve the
  problem.
• Remember, there are few factors and many
  (endless) multiples for every number.