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1 – Hamburgers and Buns At Publix, hamburgers are sold in packs of 6, and buns sold are in packs of 8. If you’re throwing a small party, and you want to buy the smallest amount of hamburgers and buns so each hamburger is in a bun, how many of each do you need? How many packs of hamburgers and how many packs of buns should you buy?

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Answer 24 Because the Least Common Multiple (LCM) of 6 and 8 is 24. You need 4 packs of hamburgers to equal 24 and you need 3 packs of buns to equal 30.

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2 - Pens and Pencils There are 42 pens and 63 pencils. All of the pens and pencils are given to the students in Language Arts. Each student receives the same number of pens and the same number of pencils. What is the largest number of students in Language Arts? How many pens and pencils will each student receive?

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Answer 21 Students Because the Greatest Common Factor (GCF) of 42 and 63 is 21. Each student will receive 2 pens and 3 pencils.

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3 - 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? How many of each fruit will be in each package?

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Answer 40 Packages Because the GCF of 160, 80, and 120 is 40. He will have 4 apples in each, 2 plums in each, and 3 pears in each package.

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4 - Football In a football game, the Mustangs scored all touchdowns and extra points, 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? How many touch downs did the Mustangs score and how many field goals did the Hoyas kick?

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

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5 - Dog Treats Milkbones come in boxes of 6, and rawhides come in bags of 9. You want to make treat boxes for the animal shelter and you want each treat box to have the same number of Milkbones and the same number of rawhides with none left over. What is the smallest number of treat boxes you could make? How many boxes of Milkbones and how many bags of rawhides do you need to buy?

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Answer 18 Treat Boxes Because the LCM of 6 and 9 is 18. You will need to buy 3 boxes of Milkbones and 2 bags of rawhides to get 18 of each.

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6 - 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 maximum number of teams that can play? How many boys will be on each team and how many girls?

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Answer 8 Teams Because the GCF of 40 and 32 is 8. There will be 5 boys and 4 girls on each team.

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7 - Coins Jonathan has 15 quarters, 30 dimes, and 48 nickels. He wants to group his money so each group has the same number of each coin. What is the most number of groups he can make? How many of each type of coin will be in each group?

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Answer 3 Groups of Coins Because the GCF of 15, 30, and 48 is 3. There will be 5 quarters, 10 dimes, and 16 nickels in each group.

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8 - 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? How many packs of pens, stickers, and bouncy balls does she need to buy?

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Answer 12 Party Bags Because the LCM of 6, 4, and 3 is 12. She will need to buy 2 packs of pens, 3 packs of stickers, and 4 packs of bouncy balls.

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Observations Notice for all of the questions which asked you to find the greatest (or a synonym of “greatest”), you found the Greatest Common Factor (GCF) of the given numbers to solve the problem. Notice for all of the questions which asked you to find the least (or synonym of “least”), you found the Least Common Multiple (LCM) of the given numbers to solve the problem. Remember, there are few factors and many (endless) multiples for every number.

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