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Least Common Multiple
Algebra Seminar2012-2013
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What is LCM?
• LCM stands for Least Common Multiple• LCM is used to find a common denominator
for two fractions in order to compare them.• LCM is defined as: the smallest number
that both numbers are factors of.
• Lets watch a short video from www.unitedstreaming.com on LCM.
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Finding the LCMLeast Common Multiple (LCM):
Method 1: Make a list of multiples
Ex: Find the LCM of 4 and 9
9: 9, 18, 27, 36, 45,
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 44
36 is the LCM of 4 and 9
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More Examples of LCMEx: Find the LCM of 10 and 12
10:12:
10, 20, 30, 40, 50, 60, 70, 80, 90, 10012, 24, 36, 48, 60, 72, 84, 96, 108
60 is the LCM of 10 and 12
Ex: Find the LCM of 6 and 8
6:8:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 728, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88
24 is the LCM of 6 and 8
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Tips for finding the Least Common Multiple
1. Make a list of multiples for each number2. Look for the smallest number they have in common3. If you are looking for the LCM of more than two numbers make more lists. The LCM must be common to ALL of the numbers.
5 = 5, 10, 15, 20, 25, 30, 35 6 = 6, 12, 18, 24, 30, 36 10 = 10, 20 , 30, 40, 50 , 60
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Put the following fractions in order from greatest to least without using a calculator:
6
1,9
5,
12
7,3
2
Using the LCM to Put Fractions in Order
Without a calculator, we cannot change the fractions to decimals. We will have to use LCM.
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Step 1: Find the LCM of the denominators
Using the LCM to Put Fractions in Order
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3: 3, 6, 9, 12, 15, 18, 21, 24, 27
30, 33, 36, 39, 42 …
6: 6, 12, 18, 24, 30, 36, 42, 48…
LCM = 36
The LCM of 6, 12, 9, and 3 is….
12: 12, 24, 36, 48 …
9: 9, 18, 27, 36, 45 …
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Step 2: Write equivalent fractions.
36x 6
x 6 6 12
736x 3
x 3 21
9
536x 4
x 4 20 3
236x 12
x 1224
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Greatest to Least
Step 3: Compare the numerators
6
1
36 6
12
73621
9
53620
3
23624
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Put the Fractions in Order
Now try this one.
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The correct answer is:
Here are some more to try.