Math lesson for junior high school for a

lesson

1. Math
August 13, 2019
Mrs. S. Whitaker

2. D.E.A.R. (9:00-9:15)
•Drop everything and
read!!!
•No talking!

3. Jaguar Ascension
•Continue writing prompt from yesterday

4. AGENDA
•Bell Ringer
•Lesson on LCM
•Activity
•Write multiplication facts #1-10
•Transition

5. Bell Ringer
Find:
•GCF of 10 and 50
•GCF of 5 and 35
•GCF of 3 and 12

6. Least Common Least Common
Multiple (LCM)Multiple (LCM)

7. Essential Question:Essential Question:
How do I find the least common multiple How do I find the least common multiple
of two or three numbers, and why is this of two or three numbers, and why is this
relevant to me?relevant to me?
Common Core Objective:Common Core Objective:
6.NS.46.NS.4
Common Core Objective:Common Core Objective:
Students will be able to identify the least common Students will be able to identify the least common
multiple of two or three one, two, and three digit multiple of two or three one, two, and three digit
numbers with 80% accuracy.numbers with 80% accuracy.
Least Common Multiple (LCM)Least Common Multiple (LCM)

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

9. When thinking about finding the Least When thinking about finding the Least
Common Multiple, or the LCM…Common Multiple, or the LCM…
REMEMBERREMEMBER
LL…The …The smallestsmallest number number
CC…all terms in …all terms in commoncommon
MM…from their list of …from their list of multiplesmultiples
Least Common Multiple (LCM)Least Common Multiple (LCM)

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

11. Finding the LCM: Method 1 – Multiple ListFinding the LCM: Method 1 – Multiple List
Example 1Example 1:: Find the LCM of 4 and 9. 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
44: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …
The LCM of 4 and 9 is 36
Least Common Multiple (LCM)Least Common Multiple (LCM)
99: 9, 18, 27, 36, 45, 54, 63,…: 9, 18, 27, 36, 45, 54, 63,…

12. Finding the LCM: Method 2 – Prime FactorizationFinding the LCM: Method 2 – Prime Factorization
Example 1Example 1:: Find the LCM of 4 and 9. 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.
44 99
LCM = 36
22
2 · 22 · 2
22
44: : 22 · · 22
99: : 33 · · 33
22 ·· 2 ·2 · 33 ·· 3 = 363 = 36
Least Common Multiple (LCM)Least Common Multiple (LCM)
33
3 · 33 · 3
33

13. Finding the LCM: Method 3 – Find the ProductFinding the LCM: Method 3 – Find the Product
Example 1Example 1:: Find the LCM of 4 and 9. 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)Least Common Multiple (LCM)

14. Finding the LCM: Method 3 – Find the ProductFinding the LCM: Method 3 – Find the Product
Example 1Example 1:: Find the LCM of 4 and 9. 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
LCM = 36
Least Common Multiple (LCM)Least Common Multiple (LCM)
44
x 9x 9
3636

15. Finding the LCM: Method 1 – Multiple ListFinding the LCM: Method 1 – Multiple List
Example 2Example 2:: Find the LCM of 10 and 12. Find the LCM of 10 and 12.
Least Common Multiple (LCM)Least Common Multiple (LCM)
Step 1: Create a list of multiple for each number
Step 2: Circle the first multiple the numbers have in common
1010: 10, 20, 30, 40, 50, 60, 70, 80,…: 10, 20, 30, 40, 50, 60, 70, 80,…
The LCM of 10 and 12 is 60
1212: 12, 24, 36, 48, 60, 72, 84,…: 12, 24, 36, 48, 60, 72, 84,…

16. Finding the LCM: Method 2 – Prime FactorizationFinding the LCM: Method 2 – Prime Factorization
Example 2Example 2:: Find the LCM of 10 and 12. Find the LCM of 10 and 12.
Step 1: Find the prime factorization of each number.
Least Common Multiple (LCM)Least Common Multiple (LCM)
Step 1: Find the prime factorization of each number.
Step 2: Find the product of all the prime factors

17. Finding the LCM: Method 2 – Prime FactorizationFinding the LCM: Method 2 – Prime Factorization
Example 2Example 2:: Find the LCM of 10 and 12. Find the LCM of 10 and 12.
Step 1: Find the prime factorization of each number.
Least Common Multiple (LCM)Least Common Multiple (LCM)
Step 1: Find the prime factorization of each number.
Step 2: Find the product of all the prime factors
1010 1212
LCM = 60
22
2 · 52 · 5
55
1010: : 22 · 5 · 5
1212: : 22 2 · 3 2 · 3
22 ·· 5 ·5 · 22 ·· 3 = 603 = 60
33
3 · 2 · 23 · 2 · 2
44
2222

18. Finding the LCM: Method 1 – Multiple ListFinding the LCM: Method 1 – Multiple List
Example 3Example 3:: Find the LCM of 12 and 16. Find the LCM of 12 and 16.
Least Common Multiple (LCM)Least Common Multiple (LCM)
Step 1: Create a list of multiple for each number
Step 2: Circle the first multiple the numbers have in common

19. Finding the LCM: Method 1 – Multiple ListFinding the LCM: Method 1 – Multiple List
Example 3Example 3:: Find the LCM of 12 and 16. Find the LCM of 12 and 16.
Least Common Multiple (LCM)Least Common Multiple (LCM)
Step 1: Create a list of multiple for each number
Step 2: Circle the first multiple the numbers have in common
The LCM of 12 and 16 is 48
1212: 12, 24, 36, 48, 60, 72, 84, 96, …: 12, 24, 36, 48, 60, 72, 84, 96, …
1616: 16, 32, 48, 64, 80, 96,…: 16, 32, 48, 64, 80, 96,…
FYI…there is always more
than one multiple for any
set of numbers

20. Finding the LCM: Method 2 – Prime FactorizationFinding the LCM: Method 2 – Prime Factorization
Example 3Example 3:: Find the LCM of 12 and 16. Find the LCM of 12 and 16.
Least Common Multiple (LCM)Least Common Multiple (LCM)
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
16161212
LCM = 48
22
2 · 2 · 2 · 22 · 2 · 2 · 2
22
1212: : 22 · · 2 2 · 3· 3
1616: : 22 · · 22 · 2 · 2 · 2 · 2
2 · 2 · 2 · 2 · 3 = 482 · 2 · 2 · 2 · 3 = 48
33
3 · 2 · 23 · 2 · 2
44
22222222
4444

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

22. Guided Practice ProblemsGuided Practice Problems
DirectionsDirections:: Find the LCM for each number set. Find the LCM for each number set.
1. 9 and 121. 9 and 12
2. 4, 8, and 122. 4, 8, and 12
3. 2, 3, 6, and 83. 2, 3, 6, and 8
Least Common Multiple (LCM)Least Common Multiple (LCM)

23. Guided Practice ProblemsGuided Practice Problems
DirectionsDirections:: Find the LCM for each number set. Find the LCM for each number set.
1. 9 and 121. 9 and 12 => => 66
2. 4, 8, and 122. 4, 8, and 12=> => 1616
3. 2, 3, 6, and 83. 2, 3, 6, and 8=> => 2424
Least Common Multiple (LCM)Least Common Multiple (LCM)

24. Independent Practice ProblemsIndependent Practice Problems
DirectionsDirections:: Find the LCM for each number set. Find the LCM for each number set.
1. 6 and 101. 6 and 10
2. 2, 4, and 5 2. 2, 4, and 5
3. 4, 6, and 83. 4, 6, and 8
Least Common Multiple (LCM)Least Common Multiple (LCM)

25. Independent Practice ProblemsIndependent Practice Problems
DirectionsDirections:: Find the LCM for each number set. Find the LCM for each number set.
1. 6 and 101. 6 and 10 => => 3030
2. 2, 4, and 5 2. 2, 4, and 5 => => 2020
3. 4, 6, and 83. 4, 6, and 8=> => 2424
Least Common Multiple (LCM)Least Common Multiple (LCM)