Download LEAST COMMON MULTIPLE (LCM)

LEAST COMMON
MULTIPLE (LCM)
Least Common Multiple (LCM)
Essential Question:
How do I find the least common multiple of two or three numbers,
and why is this relevant to me?
Common Core Objective:
6.NS.4
Common Core Objective:
Students will be able to identify the least common
multiple of two or three one, two, and three digit
numbers with 80% accuracy.
Least Common Multiple (LCM)
Vocabulary:
 Multiple – a non-zero .
 Least Common Multiple – the least non-zero
common multiple of two or more numbers.
Least Common Multiple (LCM)
When thinking about finding the Least Common Multiple, or the LCM…
REMEMBER
L…The smallest number
C…all terms in common
M…from their list of multiples
Least Common Multiple (LCM)
Important to Remember…
THREE
There are
methods for
finding the Common Multiples of two or
more numbers…
Method 1…Use Multiple Lists
Method 2…Use Prime Factorization
Method 3…Multiply the Numbers***
Least Common Multiple (LCM)
Finding the LCM: Method 1 – Multiple List
Example 1: Find the LCM of 4 and 9.
Step 1: Create a list of multiples for each number
Step 2: Circle the first multiple the numbers have in common
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …
9: 9, 18, 27, 36, 45, 54, 63,…
The LCM of 4 and 9 is 36
Least Common Multiple (LCM)
Finding the LCM: Method 2 – Prime Factorization
Example 1: Find the LCM of 4 and 9.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of all the prime factors.
4
2
9
2
2·2
3
3
3·3
4: 2 · 2
9:
3·3
2 · 2 · 3 · 3 = 36
LCM = 36
Least Common Multiple (LCM)
Finding the LCM: Method 3 – Find the Product
Example 1: Find the LCM of 4 and 9.
Step 1: For any two numbers, multiply them together
Step 2: Your answer is the LCM of the numbers
Least Common Multiple (LCM)
Finding the LCM: Method 3 – Find the Product
Example 1: Find the LCM of 4 and 9.
Step 1: For any two numbers, multiply them together
Step 2: Your answer is the LCM of the numbers
4
x9
36
LCM = 36
Least Common Multiple (LCM)
Finding the LCM: Method 1 – Multiple List
Example 2: Find the LCM of 10 and 12.
Step 1: Create a list of multiple for each number
Step 2: Circle the first multiple the numbers have in common
10: 10, 20, 30, 40, 50, 60, 70, 80,…
12: 12, 24, 36, 48, 60, 72, 84,…
The LCM of 10 and 12 is 60
Least Common Multiple (LCM)
Finding the LCM: Method 2 – Prime Factorization
Example 2: Find the LCM of 10 and 12.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of all the prime factors
Least Common Multiple (LCM)
Finding the LCM: Method 2 – Prime Factorization
Example 2: Find the LCM of 10 and 12.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of all the prime factors
10
2
12
5
2·5
3
10: 2 · 5
12: 2
2·3
4
2
2
3·2·2
2 · 5 · 2 · 3 = 60
LCM = 60
Least Common Multiple (LCM)
Finding the LCM: Method 3 – Find the Product
Example 2: Find the LCM of 10 and 12.
Step 1: For any two numbers, multiply them together
Step 2: Your answer is the LCM of the numbers
Least Common Multiple (LCM)
Finding the LCM: Method 3 – Find the Product
Example 2: Find the LCM of 10 and 12.
Step 1: For any two numbers, multiply them together
Step 2: Your answer is the LCM of the numbers
NO
10
x 12
20
+ 100
120
Common Multiple = 120
FYI…this method does not
ALWAYS give you the LCM,
sometimes it just gives you a
multiple of the numbers
Least Common Multiple (LCM)
Finding the LCM: Method 1 – Multiple List
Example 3: Find the LCM of 12 and 16.
Step 1: Create a list of multiple for each number
Step 2: Circle the first multiple the numbers have in common
Least Common Multiple (LCM)
Finding the LCM: Method 1 – Multiple List
Example 3: Find the LCM of 12 and 16.
Step 1: Create a list of multiple for each number
Step 2: Circle the first multiple the numbers have in common
12: 12, 24, 36, 48, 60, 72, 84, 96, …
16: 16, 32, 48, 64, 80, 96,…
FYI…there is always more
than one multiple for any
set of numbers
The LCM of 12 and 16 is 48
Least Common Multiple (LCM)
Finding the LCM: Method 2 – Prime Factorization
Example 3: Find the LCM of 12 and 16.
Step 1: Find the prime factorization of each number.
Step 2: Find the product of all the prime factors
12
3
16
4
2
4
4
2
3·2·2
2
12: 2 · 2 ·
3
16: 2 · 2 · 2 · 2
2 2
2·2·2·2
2
2 · 2 · 2 · 2 · 3 = 48
LCM = 48
Least Common Multiple (LCM)
Finding the LCM: Method 3 – Find the Product
Example 3: Find the LCM of 12 and 16.
Step 1: For any two numbers, multiply them together
Step 2: Your answer is the LCM of the numbers
Least Common Multiple (LCM)
Finding the LCM: Method 3 – Find the Product
Example 3: Find the LCM of 12 and 16.
Step 1: For any two numbers, multiply them together
Step 2: Your answer is the LCM of the numbers
NO
12
x 16
72
+ 120
192
Common Multiple = 192
FYI…this method does not
ALWAYS give you the LCM,
sometimes it just gives you a
multiple of the numbers
Least Common Multiple (LCM)
Important to Remember…
THREE
There are
methods for finding
the Common Multiples of two or more
numbers…
Method 1…Use Multiple Lists
Method 2…Use Prime Factorization
Method 3…Find the Product the of Numbers***
Least Common Multiple (LCM)
Guided Practice Problems
Directions: Find the LCM for each number set.
1. 9 and 12
2. 4, 8, and 12
3. 2, 3, 6, and 8
Least Common Multiple (LCM)
Guided Practice Problems
Directions: Find the LCM for each number set.
1. 9 and 12
=> 6
2. 4, 8, and 12 => 16
3. 2, 3, 6, and 8
=> 24
Least Common Multiple (LCM)
Independent Practice Problems
Directions: Find the LCM for each number set.
1. 6 and 10
2. 2, 4, and 5
3. 4, 6, and 8
Least Common Multiple (LCM)
Independent Practice Problems
Directions: Find the LCM for each number set.
1. 6 and 10
=> 30
2. 2, 4, and 5 => 20
3. 4, 6, and 8
=> 24