1. Least Common Multiple (LCM)

2. 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
Students will be able to identify the least common multiple of two or three one, two, and three digit numbers with 80% accuracy.

3. Least Common Multiple (LCM)
Vocabulary:
Multiple – a non-zero .
Least Common Multiple – the least non-zero common multiple of two or more numbers.

4. 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

5. Least Common Multiple (LCM)
Important to Remember…
There are TWO methods for finding the Common Multiples of two or more numbers…
Method 1…Use Multiple Lists
Method 2…Use Prime Factorization

6. 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

7. 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 9
4: 2 · 2
9: · 3 2 2 3 3
2 · 2
3 · 3
2 · 2 · 3 · 3 = 36
LCM = 36

8. 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

9. 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
x 9
LCM = 36 36

10. 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

11. 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 1: Find the prime factorization of each number.
Step 2: Find the product of all the prime factors

12. 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 1: Find the prime factorization of each number.
Step 2: Find the product of all the prime factors 10 12
10: 2 · 5
12: · 3 2 5 3 4 2 2
2 · 5
2 · 5 · 2 · 3 = 60
3 · 2 · 2
LCM = 60

13. 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

14. 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

15. 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 1: Find the prime factorization of each number.
Step 2: Find the product of all the prime factors 12 16
12: 2 · 2 ·
16: 2 · 2 · 2 · 2 3 4 4 4
2 · 2 · 2 · 2 · 3 = 48 2 2 2 2 2 2
3 · 2 · 2
2 · 2 · 2 · 2
LCM = 48

16. Least Common Multiple (LCM)
Important to Remember…
There are TWO methods for finding the Common Multiples of two or more numbers…
Method 1…Use Multiple Lists
Method 2…Use Prime Factorization

17. Least Common Multiple (LCM)
Guided Practice Problems
Directions: Find the LCM for each number set.
and 12
2. 4, 8, and 12
3. 2, 3, 6, and 8

18. Least Common Multiple (LCM)
Guided Practice Problems
Directions: Find the LCM for each number set.
and 12 => 6
2. 4, 8, and 12 => 16
3. 2, 3, 6, and 8 => 24

19. Least Common Multiple (LCM)
Independent Practice Problems
Directions: Find the LCM for each number set.
and 10
2. 2, 4, and 5
3. 4, 6, and 8

20. Least Common Multiple (LCM)
Independent Practice Problems
Directions: Find the LCM for each number set.
and 10 => 30
2. 2, 4, and 5 => 20
3. 4, 6, and 8 => 24