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3.1.2 GCF_and_LCM.notebook
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February 02, 2014
3.1.2 GCF_and_LCM.notebook
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February 02, 2014
Greatest Common Factor (GCF): the greatest number that divides into each number in a set.
Ex. 5 is the greatest common factor of 10 and 15
factors of 10 - 1,2,5,10 factors of 15 - 1,3,5,15
GCF
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Example 2: Determining the Greatest Common Factor
Determine the GCF of 138 and 198.Solution:Write the prime factorization of each number. Highlight the factors that appear in each prime factorization.
138= 2 . 3 . 23198= 2 . 3 . 3 . 11
The GCF is 2 . 3, which is 6.
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Check your understanding
Determine the GCF of 126 and 144.
GCF = 18Answer
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14, 56, 91 18, 54, 126
Greatest Common Factor (GCF) Example 2 p. 136 (DVD 3_1)
Determine the GCF of each set of numbers:
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14, 56, 91 18, 54, 126
STEPS:1. prime factor each number in the set
Greatest Common Factor (GCF) Example 2 p. 136 (DVD 3_1)
Determine the GCF of each set of numbers:
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14, 56, 91 18, 54, 126
STEPS:1. prime factor each number in the set2. circle the factors that are common
Greatest Common Factor (GCF) Example 2 p. 136 (DVD 3_1)
Determine the GCF of each set of numbers:
3.1.2 GCF_and_LCM.notebook
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14, 56, 91 18, 54, 126
STEPS:1. prime factor each number in the set2. circle the factors that are common3. place factors in a Venn diagram
Greatest Common Factor (GCF) Example 2 p. 136 (DVD 3_1)
Determine the GCF of each set of numbers:
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14, 56, 91 18, 54, 126
STEPS:1. prime factor each number in the set2. circle the factors that are common3. place factors in a Venn diagram4. GCF is product of common factors
Greatest Common Factor (GCF) Example 2 p. 136 (DVD 3_1)
Determine the GCF of each set of numbers:
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HOMEWORK
Page 140 # 8, 9 (a,b)
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Least Common Multiple (LCM)
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To generate multiples of a number, multiply the number by the natural
numbers (1,2,3,4,5, etc)
Ex. Some multiples of 26 are:26 . 1 = 2626 . 2 = 5226 . 3 = 78
What are some multiples of 30?30, 60, 90 ...
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For two or more natural numbers, we can determine their least common multiple.
The least common multiple (LCM) of two or more numbers is the smallest number that is divisible by each number.
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We can determine the LCM of 4 and 6 by combining identical copies of each smaller chain to create two chains of equal length.
The shortest chain possible is 12 cubes long.So, the least common multiple of 4 and 6 is 12.
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Example 3: Determining the LCM.
Determine the LCM of 18, 20 and 30.
Solutions:Method 1:List the multiples of each number until the same multiple appears in all 3 lists.Multiples of 18:Multiples of 20:Multiples of 30:
18,36,54,72,90,108,126,144,162,180
20,20,60,80,100,120,140,160,180
30,60,90,120,150,180
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Example 3: Determining the LCM. (cont'd)
Determine the LCM of 18, 20 and 30.
Solutions:Method 2:
The LCM is the product of the greatest power of each prime factor:22 . 32 . 5 = 4 . 9 . 5
= 180The LCM of 18, 20 and 30 is 180.
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Least Common Multiple (LCM) Example 3 p. 137 (DVD 3_1)
Determine the LCM of each set of numbers:14, 56, 91 18, 54, 126
STEPS:1. prime factor each number in the set2. circle the factors that are common3. place factors in a Venn diagram4. GCF is product of common factors5. LCM is product of all factors in the diagram
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Least Common Multiple (LCM) Example 3 p. 137 (DVD 3_1)
Determine the LCM of each set of numbers:14, 56, 91 18, 54, 126
STEPS:1. prime factor each number in the set2. circle the factors that are common3. place factors in a Venn diagram4. GCF is product of common factors5. LCM is product of all factors in the diagram
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Least Common Multiple (LCM) Example 3 p. 137 (DVD 3_1)
Determine the LCM of each set of numbers:14, 56, 91 18, 54, 126
STEPS:1. prime factor each number in the set2. circle the factors that are common3. place factors in a Venn diagram4. GCF is product of common factors5. LCM is product of all factors in the diagram
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Least Common Multiple (LCM) Example 3 p. 137 (DVD 3_1)
Determine the LCM of each set of numbers:14, 56, 91 18, 54, 126
STEPS:1. prime factor each number in the set2. circle the factors that are common3. place factors in a Venn diagram4. GCF is product of common factors5. LCM is product of all factors in the diagram
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Check You Understanding
Determine the LCM of 28, 42, and 63.
LCM =252Answer
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HOMEWORK
Page 140 # 10 and 11
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(GCF) AND (LCM)greatest common factor (GCF) the greatest number that divides into each number in a set. Eg. the GCF of 75, 100 & 125 is 25.
least common multiple (LCM) the least multiple that is the same for a set of numbers. Eg. the LCM of 75, 100 & 125 is 1500.KEY WORDS to look for with GCF/LCM Word problems.
GCF: largest biggest breaking an object
into parts, pieces,or groups
LCM: smallest Expanding an area
until the pieces fit. Identical grouping next time something
happens in schedule
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GCF & LCM Word ProblemsWe will use prime factorization to find the Greatest Common Factor or the Least Common Multiple in order to solve word problems.
How do I know which one I need to calculate to answer the question?
GCF if I need to make small, equal groups or sets of items from larger groups of items with no remainder
LCM when I need to find when a next occurrence is; when I need to have the same amount of different items
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What is the side length of the smallest square that could be tiled with rectangles that measure 16cm by 40cm? Assume the rectangles cannot be cut.
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What is the side length of the largest square that could be used to tile a rectangle that measures 16cm by 40cm? Assume that the squares cannot be cut.
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Examples
What I know:GCF or LCM?
#1
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What I know:GCF or LCM?
#2
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What I know:GCF or LCM?
#3
30 = 2 . 5 . 3
50 = 2 . 5 . 5 = 2 . 52
20 = 2 . 5 . 2 = 5 . 22
the greatest power of 5 in any list is 52
the greatest power of 2 in any list is 22
the greatest power of 3 in any list is 3
The LCM is the product of the greatest power of each prime factor:52 . 22 . 3 = 25 . 4 . 3 = 300
The LCM of 30, 50, and 20 is 300.
Therefore I would need to buy 300 / 30 = 10 packages of paper plates,300/50 = 6 packages of paper napkins, and 300/20 = 15 packages of paper cups.
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What I know:GCF or LCM?
#4
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Practice:
Page 140 #12, 14, 15(ab), 17
