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Least Common Multiple
LCM
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Essential Question:How do I find the least common multiple
of two or three numbers, and why is this relevant to me?
Common Core Objective:6.NS.4
Common Core Objective:Students will be able to identify the least common
multiple of two or three one, two, and three digit numbers.
Least Common Multiple (LCM)
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When thinking about finding the Least Common Multiple, or the LCM…
REMEMBER
L…The smallest number
C…all terms in common
M…from their list of multiples
Least Common Multiple (LCM)
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Important to Remember…
There are THREE methods for finding the Common Multiples of two or
more numbers…
Method 1…Use Multiple ListsMethod 2…Use Prime FactorizationMethod 3…Multiply the Numbers***
Least Common Multiple (LCM)
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Multiple
The product of a whole number
multiplied times any other whole
number.
Name the first six multiples of 6
6, 12, 18, 24, 30, 36
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Name the first six
multiples of 5
5, 10, 15, 20, 25, 30
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Common MultipleA Common Multiple is a number
that is a multiple of two numbers.
Here are common multiples for the
numbers 4 and 10
10 = 10, 20, 30, 40, 50,
4 = 4, 8, 12, 16, 20, 24
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Least Common Multiple
Smallest
number that a set of given numbers divides
evenly into.
LCM - Least Common Multiple -
It is useful to know how to do this so you
can find a common denominator when
adding or subtracting fractions.
THERE ARE TWO WAYS TO FIND LCM
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Least Common Multiple
Method # 1
TO FIND THE LCM OF TWO NUMBERS
• Find the least multiple that
both numbers have in common.
•List the multiples of both numbers
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Least Common Multiple Method # 1
Make a List of Multiples
Find the LCM of 10 and 12.
10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
12: 12, 24, 36, 48, 60
LCM = 60
...
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Least Common Multiple Method # 1
Make a List of Multiples
Find the LCM of 32 and 40.
32: 32 , 64, 96, 128, 160, 192, 224, 256
40: 40, 80, 120, 160
LCM = 160
...
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What is the Least Common
Multiple of 4 & 10
10 = 10, 20, 30, 40, 50,
4 = 4, 8, 12, 16, 20, 24
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What is the Least Common
Multiple of 6 & 8
8 = 8, 16, 24, 32, 40, 48
6 = 6, 12, 18, 24, 30, 36
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What is the Least Common
Multiple of 3 & 9
9 = 9, 18, 27, 36, 45, 54
3 = 3, 6, 9, 12, 15, 21,
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Guided Practice ProblemsDirections: Find the LCM for each number set.
1. 9 and 12
2. 4, 8, and 12
3. 2, 3, 6, and 8
Least Common Multiple (LCM)
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Independent Practice ProblemsDirections: Find the LCM for each number set.
1. 6 and 10
2. 2, 4, and 5
3. 4, 6, and 8
Least Common Multiple (LCM)
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Method #1 is easy to do!
Method #1 is a good method if both of your
numbers are really small.
What if you have really large numbers? It
might take too long to keep listing
multiples until you find a common
multiple.SO HERE IS METHOD # 2
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1) Write the prime factorization of
each number.
3) Then select the remaining factors
and multiply.
2) Select all common factors ONCE.
Least Common Multiple Method # 2
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20
2 10
2 5
2 2 5
18
2 9
3 3
2 3 3
Select all common factors once.
LCM 2
Then select the remaining factors.
3 3 2 5
LCM 180
Least Common Multiple Method # 2
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2 2 2 3 3
45
5 9
3 3
3 3 5
Select all common factors once.
LCM 3Then select the remaining factors.
3 5 2 2
LCM 360
72
8 9
3 32 4
2 2
2
Least Common Multiple Method # 2
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Find the LCM of 48 and 80.
48 802
24 402
12 202
6 102
3 5
Common FactorsOnce
Remaining Factors
LCM
LCM 240
2 3222 5
Least Common Multiple Method # 2
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SO I GUESS YOU ARE WONDERING
When Are We Ever Gonna
Have To Use This?
Least Common Multiple Method # 2
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What is the LCM used for?The LCM is used to find common denominatorsso that fractions may be easily compared, added,or subtracted.
5
8
7
12
8 1224 622 3
LCM 2 2 2 3
LCM 24
24 24
15 14
33 2
2
Least Common Multiple Method # 2
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#9 MultiplesA number that is added to itself
becomes a multiple.
Multiples of 3 = 3, 6, 9, 12, 15, 18 . . .
Multiples can go on infinitely forever.
It is useful to know this for adding fractions.
The least common multiple (LCM) is the
least common number that is a multiple of 2
numbers.
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LCM Make a List Method # 1
TO FIND THE LCM OF 4 and 12:
2) Find the least multiple that both numbers have in common.
1) List the multiples of both numbers
4 = 4, 8, 12, 16, 20…
12 = 12, 24, 36…
LCM is 12
#10
This method is useful if both numbers are small.
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1) List the prime factorization to find the LCM.
20
2 10
2 5
2 2 5
18
2 9
3 3
2 3 3
2) Select all common factors once.
LCM 2
3) Select all remaining factors, and multiply.
3 3 2 5 LCM 180
#11 LCM Prime Factorization Method # 2
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