Least Common Multiple

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Least Common Multiple
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What is a multiple?

• A multiple of a whole number is the product of
  the whole number and any number
• Example the multiples of 8 are
• 8 x 1 8
• 8 x 2 16
• 8 x 3 24
• 8 x 4 32

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What are the multiples of 5?
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What are the multiples of 8?
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What is a LCM?

• LCM is the smallest number other than 0 that is a
  multiple of 2 or more whole numbers

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Find the LCM by making a list

• List all the nonzero multiples
• 9 9, 18, 27, 36, 45, 54, 63, 72
• 12 12, 24, 36, 48, 60, 72
• Identify the LCM from the list
• The LCM of 9 and 12 is 36.

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HINTS

• The LCM cannot be larger than the product of the
  two whole numbers.
• 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

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A quick review What is prime factorization?

• A composite number expressed as a product of
  primes
• Factor Trees
• 15
• 3 5

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Find the LCM by using prime factorization

• Find the LCM of 15 and 25
• 15 25
• 5 3 5 5

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15 and 25 cont.

• Identify common factors
• 15 3, 5
• 25 5, 5
• Find the product of the common and remaining
  factors
• 3 x 5 x 5 75

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School Dance Team

• 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?

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To find the number of members needed you find the
LCM for 3, 4 or 5
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Use the list method
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Using prime factorization
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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?

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List Method
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Prime Factorization
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• The bags will have the same weight at 2 ? 2 ? 2 ?
  3 ? 3 or 72 ounces.
•  

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On a calculator

• 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
• Enter 1st number
• 2nd key
• . (,)
• Enter 2nd number
• )
• Enter