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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?

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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.

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Pens and Pencils There are 42 pens and 63 pencils. All of the pens and pencils are given to the students in Mrs. Burchette’s 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?

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

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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?

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

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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?

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

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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?

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

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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?

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

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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?

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

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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?

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

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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.

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Greatest Common Factor Least Common Multiple

Greatest Common Factor Least Common Multiple

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