1. Do Now 12/7/10 Take out HW from last night. Copy HW in your planner.
Text page 185, #12-36 evens; #42-46 evens
Copy HW in your planner.
Text page 190, #16-36 evens
In your journal, explain how you simplify fractions. Then simplify the following variable expression.

2. Homework Text page 185, #12-36 evens; #42-46 evens
30) 2mn / 5
32) st / 8
34) 3r / 4
36) 7 / t
42) 9/10, 9/10; yes
44) 3/4, 3/4; yes
46) 5/6, 19/24; no
12) 1/2, 12/24
14) 7/8, 28/32
16) 4/5, 32/40
18) 14/20, 21/30
20) 8/9
22) 23/36
24) 9/10
26) 13/14
28) a) 40/ b) 63/103

3. Objective
SWBAT find the least common multiple of two numbers.

4. Section 4.4 “Least Common Multiple”
A multiple of a number is the product of the number and any other number greater than zero.
What are the multiples of 5?
Think of counting by fives…
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 …
Least Common Multiple
Of all the common multiples of two numbers, the smallest is the least common multiple.

5. Least Common Multiple Find the LCM of 6 and 9.
List the multiples of the two numbers and then compare.
6: 6, 12, 18, 24, 30, 36, 42
9: 9, 18, 27, 36, 45, 54
From the list you can see that 18 and 36 are common multiples
6 and 9. Of these 18 is the least common multiple.

6. Least Common Multiple Find the LCM of 4, 6, and 8.
List the multiples of the three numbers and then compare.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52
6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
8: 8, 16, 24, 32, 40, 48, 56, 64
From the list you can see that 24 and 48 are common multiples
4,6, and 8. Of these 24 is the least common multiple.

7. Least Common Multiple Find the LCM of 64 and 72.
When the numbers are too large to list the multiples
of the two numbers, find the prime factorization of each
number. The LCM is the product of the common prime
factors and the factors that are not common.
Common
Factors
Not Common
Factors
64: 2 · 2 · 2 · 2 · 2 · 2
2 · 2 · 2
3 · 3
2 · 2 · 2
72: 2 · 2 · 2 · 3 · 3
From the list you can see that 2, 2, and 2 are common prime
factors, and the factors that are not common are 2, 2, 2, 3, and 3.
The LCM is then 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 which is 576.

8. Least Common Multiple Find the LCM of 180 and 378.
When the numbers are too large to list the multiples
of the two numbers, find the prime factorization of each
number. The LCM is the product of the common prime
factors and the factors that are not common.
Common
Factors
Not Common
Factors
180: 2 · 2 · 3 · 3 · 5
2 · 3 · · 5
3 · 7
378: 2 · 3 · 3 · 3 · 7
From the list you can see that 2, 3, and 3 are common prime
Factors, and the factors that are not common are 2, 3, 5, and 7.
The LCM is then 2 · 3 · 3 · 2 · 5 · 3 · 7 which is 3780.

9. Least Common Multiple Find the LCM of 6, 8, and 20. 6: 2 · 3 2 · 3 · 5
When you have three or more numbers,
the common prime factors may only be shared
by two of the numbers. The LCM is the product of the
common prime factors and the factors that are not common.
Common
Factors
Not Common
Factors
6: 2 · 3
2 · 3 · 5
2 · 2
8: 2 · 2 · 2
20: 2 · 2 · 5
From the list you can see that 2 and 2 are common prime
factors, and the factors that are not common are 2, 3, and 5.
The LCM is then 2 · 2 · 2 · 3 · 5 which is 120.

10. Least Common Multiple Find the LCM of 15, 30, and 50. 15: 3 · 5 5
When you have three or more numbers,
the common prime factors may only be shared
by two of the numbers. The LCM is the product of the
common prime factors and the factors that are not common.
Common
Factors
Not Common
Factors
15: · 5 5
2 · 3 · 5
30: 2 · 3 · 5
50: 2 · 5 · 5
From the list you can see that 2, 3, and 5 are common prime
factors, and the factor that is not common is 5.
The LCM is then 2 · 3 · 5 · 5 which is 150.

11. Least Common Multiple Find the LCM of 10ab and 6b. 10ab: 2 · 5 · a · b
The LCM is the product of the common prime
factors and the factors that are not common.
Common
Factors
Not Common
Factors
10ab: 2 · 5 · a · b
2 · b · a 3
6b: 2 · 3 · b
From the list you can see that 2 and b are common prime
factors, and the factors that are not common are 3, 5, and a.
The LCM is then 2 · b · 5 · a · 3 which is 30ab.

12. Least Common Multiple Find the LCM of 2a³b and 3ab.5
The LCM is the product of the common prime
factors and the factors that are not common.
Common Factors
Not Common Factors
2a³b : 2 · a · a · a · b
a · b · a · a
3 · b · b · b · b 5
3ab : 3 · a · b · b · b · b · b
From the list you can see that a and b are common prime
factors, and the factors that are not common are 2, 3, a, a, b,
b, b, and b. The LCM is then a · b · 2 · a · a · 3 · b · b · b · b
which is 6a³b. 5

13. Homework
Text page 190, #16-36 evens