GCF and LCM

GCF and LCM

Review and Reteach

When to use GCF

• to divide things into smaller sections

• to equally distribute sets of items

• to arrange something into rows or groups

• when you see - greatest number of, how many, share, no leftovers

  
  
  
  
  

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What are the 3 methods of finding GCF?

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Find the GCF of 24 and 36

List the factors of 24 and 36

24-1,2,3,4,6,8,12,24
36-1,2,3,4,9,12,18,36
Greatest Factor in Common = 12

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Find the GCF of 18 and 27.

List factors of 18 and 27

18-1,2,3,6,9,18
27-1,3,9,27
Largest factor in common = 9

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Find the GCF of 24, 48, and 84

List factors of 24, 48, 84

24-1,2,3,4,6,8,12,24
48-1,2,3,4,6,8,12,16,24,48
84-1,2,3,4,6,7,12,14,21,28,42,48
GCF = 12

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Kim is making flower arrangements. She has 16 red roses and 20 pink roses. Each arrangement MUST have the same number of red roses and the same number of pink roses. What is the greatest number of arrangements Kim can make if every flower is used?

Factors of 16 and 20

16-1,2,4,8,16
20-1,2,4,5,10,20
Greatest Common Factor - 4

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Ms. Lou is making balloon bouquets. She has 32 black balloons, 24 yellow balloons, and 16 white balloons. Each bouquet must have the same number of each color. What is the greatest number of bouquets that she can make if every balloon is used?

Factors of 32, 24, and 16

32-1,2,4,8,16,32
24-1,2,3,4,6,8,12,24
16-1,2,4,8,16
GCF = 8

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Two pieces of ribbon, one with a length of 63 inches and one with a length of 42 inches are cut into pieces of equal length with no ribbon remaining. Find the greatest possible length the pieces can be.

Factors of 63 and 42

63-1,3,7,9,21,63
42-1,2,3,6,7,14,21,42

GCF = 21

When to use LCM

• when an event will be repeating over and over

• to figure out when something will happen again at the same time

• when you see - least number of, happen at the same time, smallest number, cycle, repetition

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What are the 3 ways to find LCM?

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Find the LCM of 3 and 5

Multiples of 3 and 5

3-3,6,9,12,15
5-5,10,15
Smallest multiple in common = 15

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Find the LCM of 6 and 16

Multiples of 6 and 16

6-6,12,18,24,30,36,42,48
16-16,32,48

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Find the LCM of 3, 6, and 9

Multiples of 3, 6, and 9

3-3,6,9,12,15,18
6-6,12,18
9-9,18
LCM=18

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Juice comes in packs of 6 and granola bars in packs of 8. If there are 24 players, what is the least number of packs needed so that each player gets a drink and a granola bar?

Multiples of 6 and 8

6-6,12,18,24
8-8,16,24
LCM=24
6 x ? = 24  4
8 x ? = 24   3

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Bus A arrives at the station every 3 minutes. Bus B arrives every 7 minutes. If both buses are arriving now, how many minutes until they arrive at the same time again?

Multiples of 3 and 7

3-3,6,9,12,15,18,21
7-7,14,21
LCM=21

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A group of students are going on a field trip. They can be in groups of 40 or 60 with no one left out. Find the smallest number of students going on the field trip.

Multiples of 40 and 60

40-40, 80,120
60-60,120
LCM=120