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Least Common Multiple
LCM
2 Methods
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Product
The answer to a multiplication problem.
6 X 6 = 36
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What is the product?
7 X 8 = 56
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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 Multiple A 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
Smallestnumber that a set of given numbers dividesevenly 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 # 1TO 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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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 2Then select the remaining factors.
3 3 2 5LCM 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 2LCM 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 80224 40212 2026 1023 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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The GCF and LCM are used so regularly thatmost people find them mentally.
GCF = 1
LCM = 72
GCF = 5
LCM = 60
1) 8 9 2) 15 20
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Least Common Multiple Method # 2
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The GCF and LCM are used so regularly thatmost people find them mentally.
GCF = 4
LCM = 60
GCF = 4
LCM = 24
1) 12 20 2) 8 12
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Least Common Multiple Method # 2
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THE ENDTake Out Your Study Guide!!!
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.
202 10
2 5
2 2 5
182 9
3 3
2 3 3
2) Select all common factors once.
LCM 23) Select all remaining factors, and multiply.
3 3 2 5 LCM 180
#11 LCM Prime Factorization Method # 2