Least Common Multiple (LCM)

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Least Common Multiple(LCM)
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• Definition
• The smallest postive number that is a multiple of
  two or more given numbers.

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Method 1 Make a List

• STEP 1 List the first 10 multiples of the
  greater number.
•  
• STEP 2 List the multiples of the lesser number.
  Stop when you get to a multiple that was in
  your first list.
•  
• NOTE You may find that after listing several
  multiples for the lesser number that you still do
  not have a common multiple. If this is the case,
  list the next 10 multiples of the greater number
  and then continue your list for the lesser number.

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Example 1

• Find the least common multiple of 6 and 9
•  
• Multiples of 9 _____________________________
•  
• Multiples of 6 _____________________________
•  
• Least Common Multiple of 6 and 9 __

9, 18, 27, 36, 45, 54, 63, 72, 81, 90
6, 12, 18
18
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Example 2

• Find the least common multiple of 5, 8, and 10.
• Multiples of 10 ____________________________
• Multiples of 8 ____________________________
• Least Common Multiple of 5, 8, and 10 __

10, 20, 30, 40, 50, 60, 70, 80, 90, 100
8, 16, 24, 32, 40
Since you have a common multiple for 10 and 8,
ask yourself, is that number is also a multiple
of 5? If it is you have the LCM, if not continue
to the next common multiple of 10 and 8.
40
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Method 2 Upside Down Cake

• This will be very similar to how we found the
  GCF but there is an added twist at the end

Example 1 Find the LCM(10,12)
Find the GCF of the numbers given
10 12
2
5 6
Multiply each of the numbers circled to find the
LCM. 2 5 6 60 ? the LCM of 10 and 12 is 60
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Method 2 Upside Down Cake
Example 2 Find the LCM(15,25)
15 25
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Find the GCF of the numbers given
3 5
Multiply each of the numbers circled to find the
LCM. 5 3 5 75 ? the LCM of 15 and 25 is 75
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Method 2 Upside Down Cake
Example 3 Find the LCM(6,8,12)
6 8 12
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Find the GCF of the numbers given
3 4 6
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Since two of the numbers share a factor continue
Since two of the numbers share a factor continue
3 2 3
3
1 2 1
Multiply each of the numbers circled to find the
LCM. 2 2 3 1 2 1 24 ? the LCM of 6,
8, and 12 is 24
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• PAY ATTENTION!!!!
• IF THE NUMBERS HAVE A gcF OF 1, THEN THE LCM IS
  THE PRODUCT OF ALL THE NUMBERS MULTIPLIED
  TOGETHER!!!!
• Example LCM(2,5,13) The GCF of these numbers
  is 1
• 2 5 13 130

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• Rod helped his mom plant a vegetable garden. Rod
  planted a row every 30 minutes, and his mom
  planted a row every 20 minutes. If they started
  together, how long will it be before they both
  finish a row at the same time?

  Least Common Multiple of 30 and 20 ________
60 minutes
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• Three bike riders ride around a circular path.
  The first rider circles the path in 4 minutes,
  the second in 9 minutes, and the third in 12
  minutes. If they all start at the same place at
  the same time, and go in the same direction,
  after how many minutes will they meet at the
  starting point?

  Least Common Multiple of 4, 9, and 12 ________
36 minutes