Transcript Least Common Multiple LCM 2 Methods

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
4 = 4, 8, 12, 16, 20, 24
10 = 10, 20, 30, 40, 50,
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Least Common Multiple
LCM - Least Common Multiple - Smallest
number that a set of given numbers divides
evenly into.
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
•List the multiples of both numbers
• Find the least multiple that
both numbers have in common.
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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
4 = 4, 8, 12, 16, 20, 24
10 = 10, 20, 30, 40, 50,
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What is the Least Common
Multiple of 6 & 8
6 = 6, 12, 18, 24, 30, 36
8 = 8, 16, 24, 32, 40, 48
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What is the Least Common
Multiple of 3 & 9
3 = 3, 6, 9, 12, 15, 21,
9 = 9, 18, 27, 36, 45, 54
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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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Least Common Multiple Method # 2
1) Write the prime factorization of
each number.
2) Select all common factors ONCE.
3) Then select the remaining factors
and multiply.
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Least Common Multiple Method # 2
18
2
20
2 10
9
3
3
2 33
2
5
225
Select all common factors once.
Then select the remaining factors.
LCM  2 3 3 2 5
LCM  180
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Least Common Multiple Method # 2
45
5
72
9
3
8
3
335
9
2 4 3 3
2 2
2  2  2 33
Select all common factors once.
Then select the remaining factors.
LCM  3 3 5 2 2 2
LCM  360
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Least Common Multiple Method # 2
Find the LCM of 48 and 80.
48
2
Common
2 24
Factors
2 12
Once
2 6
3
80
40
20
10
5
Remaining
Factors
LCM  2 2 2 2 3 5
LCM  240
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Least Common Multiple Method # 2
SO I GUESS YOU ARE WONDERING
When Are We Ever Gonna
Have To Use This?
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Least Common Multiple Method # 2
What is the LCM used for?
The LCM is used to find common denominators
so that fractions may be easily compared, added,
or subtracted.

3 5
3 8
15
24

7 2
12 2
2 8
2 4
2
12
6
3
LCM  2  2  2  3
LCM  24
14
24
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Least Common Multiple Method # 2
The GCF and LCM are used so regularly that
most people find them mentally.
GCF = 1
1)
8
GCF = 5
9
2)
LCM = 72
15
20
LCM = 60
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Least Common Multiple Method # 2
The GCF and LCM are used so regularly that
most people find them mentally.
GCF = 4
1)
12
GCF = 4
20
2)
LCM = 60
8
12
LCM = 24
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Least Common Multiple Method # 2
THE END
Take Out Your Study Guide!!!
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#9
Multiples
A number that is added to itself
becomes a multiple.
Multiples of 3 = 3, 6, 9, 12, 15, 18 .
..
Multiples can go on infinitely forever.
The least common multiple (LCM) is the
least common number that is a multiple of 2
numbers.
It is useful to know this for adding fractions.
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#10
LCM Make a List Method # 1
TO FIND THE LCM OF 4 and 12:
1) List the multiples of both numbers
4 = 4, 8, 12, 16, 20…
12 = 12, 24, 36…
2) Find the least multiple that
both numbers have in common.
LCM is 12
This method is useful if both numbers are small.
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#11 LCM Prime Factorization Method # 2
1) List
the prime factorization to find the LCM.
20
18
2
2 10
9
3
3
2
2 33
2)
3)
5
225
Select all common factors once.
Select all remaining factors, and multiply.
LCM  180
LCM  2 3 3 2 5
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