Greatest Common Factor and Least Common Multiple
Story Problems
Directions: Identify if you should find the GCF or the LCM for each problem and then solve.
If you need to divide into smaller groups to solve, the strategy should be GCF. If you need to
make your original numbers larger, the strategy should be LCM.
1) A florist has 36 roses, 27 tulips, and 18 carnations she must use to create
bouquets. What is the largest number of bouquets the florist can create and still
Have the same number of roses, tulips and carnations in each bouquet? How
many of each kind of flower will be in each bouquet?
2) Say you have 60 pencils, 90 pens and 120 notebooks and you want to make
packages of pencils, pens and notebooks to donate to your school for students who
cannot afford these supplies. What is the maximum number of packages you can
make with each package having the same number of each item inside? How many
Pencils, pens and notebooks will be inside each package?
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 thir starting point together if they start at the same time and
maintain their jogging pace?
3)
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4) During the summer months, one ice cream truck visits Jeannette's neighborhood
every 4 days and another ice cream truck visits her neighborhood every 7 days. If
both trucks visited today, when is the next time both trucks will visit on the same day?
5) If Hank gets a haircut every 4 weeks and Frank gets one every 5 weeks and they
are both getting one today, how many weeks will it be before they are getting a haircut
on the same day again?
6)Hamburger buns come in packages of 12. Hamburger patties come in packages
of 10. Marquis would like to buy the least amount of hamburger patties and buns
and have exactly enough to have one bun for each patty. How many packages
of hamburger buns and hamburger patties must he buy?
7) Malik has 28 red marbles and he has 35 blue marbles. Malik wants to divide the
marbles up into even numbered groups. How many marbles could he place in each
group so there would be the same number in the red groups as well as the blue
groups?
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Greatest Common Factor and Least Common Multiple
Story Problems
Directions: Identify if you should find the GCF or the LCM for each problem and then solve.
If you need to divide into smaller groups to solve, the strategy should be GCF. If you need to
make your original numbers larger, the strategy should be LCM.
1) A florist has 36 roses, 27 tulips, and 18 carnations she must use to create
bouquets. What is the largest number of bouquets the florist can create and still
Have the same number of roses, tulips and carnations in each bouquet? How
many of each kind of flower will be in each bouquet?
9
36, 27, 18
4, 3 ,2
With the amount of each flower given, a florist can make
a maximum of 9 bouquets. Each bouquet will have exactly
4 roses, 3 tulips and 2 carnations. We can solve this
problem by finding the GCF of 36, 27 and 18.
2) Say you have 60 pencils, 90 pens and 120 notebooks and you want to make
packages of pencils, pens and notebooks to donate to your school for students who
cannot afford these supplies. What is the maximum number of packages you can
make with each package having the same number of each item inside? How many
Pencils, pens and notebooks will be inside each package?
30
60, 90 ,120
2, 3, 4
A person can make 30 packages and have the same number
of items in each of the packages. There would be exactly
2 pencils, 3 pens and 4 notebooks in each of the 30 packages.
This problem can be solved by finding the GCF of 60, 90 and 120.
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 thir starting point together if they start at the same time and
maintain their jogging pace?
3)
6 , 12 , 18 , 24
8 , 16 , 24
440 is a number which is not important to this problem.
Using the least common multiple of 6 and 8, we can
see that the 2 runners will end up at the beginning of
the track in 24 minutes. It will take one runner three laps
and the other four.
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4) During the summer months, one ice cream truck visits Jeannette's neighborhood
every 4 days and another ice cream truck visits her neighborhood every 7 days. If
both trucks visited today, when is the next time both trucks will visit on the same day?
Ice Cream Truck A - 4 , 8 , 12 , 16 , 20 ,24 , 28
Ice Cream Truck B - 7 , 14 , 21 , 28
It will be 28 days before the two trucks
will be in her neighborhood on the
same day.
5) If Hank gets a haircut every 4 weeks and Frank gets one every 5 weeks and they
are both getting one today, how many weeks will it be before they are getting a haircut
on the same day again?
Hank - 4 , 8 , 12 , 16 , 20
It will be 20 days before Hank and Frank
receive a haircut on the same day.
Frank - 5 , 10 , 15 , 20
6)Hamburger buns come in packages of 12. Hamburger patties come in packages
of 10. Marquis would like to buy the least amount of hamburger patties and buns
and have exactly enough to have one bun for each patty. How many packages
of hamburger buns and hamburger patties must he buy?
Packs of Buns
1
2
3
4
5
6
Hamburger Buns - 12 , 24 , 36 , 48 , 60
Hot Dog Bums -
10 , 20 , 30 , 40 , 50 , 60
Marquis will have to buy 5 packs
of hamburger buns and 6 packs of
how dog buns.
7) Malik has 28 red marbles and he has 35 blue marbles. Malik wants to divide the
marbles up into even numbered groups. How many marbles could he place in each
group so there would be the same number in the red groups as well as the blue
groups?
Red Marbles
Blue Marbles
7
Malik can create 7 groups of marbles.
Each group would contain 9 marbles. 5 of
the marbles will be blue and 4 will be red.
28 , 35
4, 5
Number of
groups created.
Number of marbles in each group.
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