Transcript Least Common Multiple

Least Common
Multiple
What is a multiple?
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A multiple of a whole number is the
product of the whole number and any
number
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Example the multiples of 8 are
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8
8
8
8
x
x
x
x
1
2
3
4
=
=
=
=
8
16
24
32
What are the multiples of 5?
What are the multiples of 8?
What is a LCM?
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LCM is the smallest number other than
0 that is a multiple of 2 or more whole
numbers
Find the LCM by making a list
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List all the nonzero multiples
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9: 9, 18, 27, 36, 45, 54, 63, 72
12: 12, 24, 36, 48, 60, 72
Identify the LCM from the list
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The LCM of 9 and 12 is 36.
HINTS
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The LCM cannot be larger than the
product of the two whole numbers.
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The LCM of 3 and 4 cannot be larger than
12 because 3 x 4 = 12
Use your multiplication chart to help
find the multiples
A quick review
What is prime factorization?
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A composite number expressed as a
product of primes
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Factor Trees
15
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3
5
Find the LCM by using prime
factorization
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Find the LCM of 15 and 25
15
5
25
3
5
5
15 and 25 cont.
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Identify common factors
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15: 3, 5
25: 5, 5
Find the product of the common and
remaining factors
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3 x 5 x 5 = 75
School Dance Team
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The school dance team lines up in even
rows of 3, 4, or 5 at practice. What is
the least number of people needed to
line up in rows or 3, 4, or 5?
To find the number of members
needed you find the LCM for 3, 4 or 5
Use the list method
Using prime factorization
Fruit word problem
Jessica is filling bags of fruit. She fills
one bag with just apples, a second bag
with just oranges, and a third bag with
just pears. If each apple weighs 6
ounces, each orange weighs 8 ounces,
and each pear weighs 9 ounces, at what
point will each of the bags have the
same weight?
List Method
Prime Factorization
The bags will have the same weight at 2
 2  2  3  3 or 72 ounces.
On a calculator
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TI 34 II
2nd key
) (math)
Arrow over to lcm
Enter key
Enter 1st number
2nd key
Division key (,)
Enter 2nd number
)
TI 34 II Multiview
 Math key
 Enter
st
 Enter 1 number
 2nd key
 . (,)
 Enter 2nd number
 )
 Enter