5'4 Least Common Multiple

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5.4 Least Common Multiple
2
Finding a Common Multiple
A multiple shared by 2 or more numbers is called
a common multiple.
Examples of multiples
2
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24,
5
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60,
8
8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, .
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Finding a Common Multiple Continued
To find a common multiple between 2 or more
numbers, you can choose between 2 methods.
Method 1 Listing Multiples
Step 1 List multiples of each number.
2
2, 4, 6, 8, 10
Step 2 Circle the smallest common number in
both set of multiples.
3
3, 6, 9, 12, 15, 18
LCM 6
Tip If you multiply the 2 numbers together,
that number is how far you need to list each
multiple out to.
6
6, 12, 18, 24, 30, 36
18
18, 36, 54
LCM 18
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Finding a Common Multiple Continued
Method 2 Prime Factorization (Factor Trees)
2
3
Because 2 and 3 are both prime numbers, simply
multiply them together. LCM 6
6
18
2
3
3
6
6
2 x 3
3
2
3
18
2 x 3 x 3
LCM 18
2 x 3 x 3 18
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Lets Do More Examples!
Find the least common multiple of 9 and 12.
Method 1 Listing Multiples
No matter what method you choose, you get
the same answer.
9
9, 18, 27, 36, 45, 54, 63, 72, 81
12
12, 24, 36, 48
LCM 36
Method 2 Prime Factorization (Factor Trees)
9
12
9
3 x 3
3
3
3
4
12
2 x 2 x 3
3
2
2
2 x 2 x 3 x 3 36
LCM 36
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More Examples Continued.
Find the LCM of 42 and 60.
Method 1 Listing
42
42, 84, 126, 168, 210, 252, 294, 336, 378, 420
60
60, 120, 180, 240, 300, 360, 420, 480
LCM 420
The next slide shows the same numbers using
factor trees.
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More Examples Continued
Find the LCM of 42 and 60.
Method 2 Prime Factorization (Factor Trees)
42
60
6
7
6
10
2
3
2
5
2
3
7
42
2 x 3 x 7
60
2 x 2 x 5
LCM 420
X 3
2 x 2 x 3 x 5 x 7 420
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Now You Try!
Find the LCM for 15 and 18 using either method.
Listing
15
15, 30, 45, 60, 75, 90, 105
LCM 90
18
18, 36, 54, 72, 90, 108, 126
Factor Trees
15
18
3
5
3
6
15
3 x 5
3
2
3
18
2 x 3 x 3
2 x 3 x 3 x 5 90
LCM 90
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Now You Try Continued
Find the LCM 16 and 20 using either method.
Listing
16
16, 32, 48, 64, 80, 96, 112, 128, 144
LCM 80
20
20, 40, 60, 80, 100, 120, 140, 160
Factor Trees
16
20
16
2 x 2 x 2 x 2
5
4
4
4
20
2 x 2 x 5
5
2
2
2 x 2 x 2 x 2 x 5
2
2
2
2
LCM 80