Word Problems HCF A florist has 36 roses, 27 tulips, and 18 carnations she must use to create bouquets. What is the largest number of bouquets she can make without having any flowers left over? The HCF is the number we're looking for, the remaining factors in each number tell us how may of each to put in each bouquet. • roses: 36 = 22 x 32 • tulips: 27 = 33 • carnations: 18 = 32 HCF = 32 = 9 bouquets (smallest exponent of 3 is 2) each bouquet will have • roses: 36 : 9 = 4 • tulips: 27 : 9 = 3 • carnations: 18 : 9 = 2 Say you have 60 pencils, 90 pens and 120 books and you want to make packages of pencils, pens and books to donate to your school for students who cannot afford these supplies. What is the maximum number of packages you can make using all items, and how many pencils, pens and books will be in each package? • pencils: 22 x 3 x 5 • pens: 2 x 32 x 5 • books: 23 x 3 x 5 • HCF = 2 x 3 x 5 = 30 packages content of each package • Pencils = 60 : 30 = 2 pencils • Pens = 90 : 30 = 3 pens • Books = 120 : 30 = 4 books • Each package with 2 pencils, 3 pens, and 4 books in each package. Try this! Dean baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her friends at school. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookie. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need? LCM You and your three friends go to lunch and find a deal on packages of 6 tacos. You want to buy the minimum number of packages so you each get the same number of tacos and none are left over. How many packages must you buy? the LCM of 4 and 6? 4 = 22 6=2x3 LCM = 22 x 3 = 12. 12 tacos requires 2 packages and you each will get 3 tacos. One trip around a running track is 440 yards. One jogger can complete one lap in 8 minutes, the other can complete it in 6 minutes. How long will it take for both joggers to arrive at their starting point together if they start at the same time and maintain their jogging pace? LCM of 6 and 8? 6=2x3 8 = 23 LCM = 23 x 3 = 24 minutes • the slower jogger will have completed 3 laps ( 24 : 8 = 3) • the faster jogger will have completed 4 laps ( 24 : 6 = 4) Try this! Bridget has swimming lessons every fifth day and diving lessons every third day. If she had a swimming lesson and a diving lesson on May 5, when will be the next date on which she has both swimming and diving lessons? Is it a HCF or LCM word problems? Frank is buying Hot Dogs for a class picnic. Hot dogs are sold in pckgs of 10. Hot Dog buns are sold in pckgs of 8. What is the smallest number of hot dogs and buns Frank can buy to have an equal number of each? You are making pumpkin pies for the bake sale. Piecrusts are sold in pckgs of 3. Pie filling is sold in 4-can pckgs. What is the least number of piecrusts and filling that you can buy to have the same number of each? Thrift market sells apple juice in 8oz containers, pineapple juice in 12 oz containers and grape juice in 16 oz containers. If Mark wants to have the same amount of each juice to make some punch, what is the least amount of ounces he should buy of each flavor of fruit juice? Mr. Brackett works in factory with his two sons. He is really happy with his job because he gets to spend some time with his beloved sons not only at home but also at work! He is allowed to take a break every 140 minutes while his two sons are allowed to take breaks in 210 minutes and 280 minutes. How many minutes will they have to wait after their first break together to get together again? Mrs.Flynn has baked 84 raisin cookies, 106 muffins and 128 chocolate chip cookies, which all smell delicious! They smell so good she would like to keep 4 raisin cookies, 6 muffins and 8 chocolate chip cookies for herself though she know she has to cut down on sweets. She'll then put the rest into boxes with equal numbers of each type. What would be the largest number of cookies or muffins in each box?