1. Do Now 12/7/09 Take out HW from last night. Copy HW in your planner.
Text page 190, #16-36 evens
Copy HW in your planner.
Text page 190, #40-68 evens
Be ready to copy POTW #4

2. Homework Text page 190, #16-36 evens
16) 36
18) 16
20) 42
22) 165
24) 12
26) 420
28) 80a³
30) 51b³
32) 120s
34) 200a²
36) 24 figures 4

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 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.

6. 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.

7. 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.

8. 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

9. Least Common Denominator
The LCD of two or more fractions is the least common multiple of the denominators. Use the LCD to compare and order fractions.

10. “Using the LCD” = = = = = Compare the fractions and .
List the equivalent fractions and find two with the same denominator. Then compare. = =
same denominator,
now compare
Therefore, 3/4 is
greater than 2/3. = = =

11. Compare the Following Fractions
<
>
<

12. Order the fractions from least to greatest.
Find the LCD for 4, 9, & 15.
LCD = 180
Rewrite equivalent fractions using the LCD.

13. Order the fractions from least to greatest.
Find the LCD for 6, 9, & 3.
LCD = 18
Rewrite equivalent fractions using the LCD.

14. Rewrite the variable expressions with a common denominator.
Find the LCD for 5b and 4ab².
LCD = 20ab²
Rewrite equivalent fractions using the LCD.

15. Rewrite the variable expressions with a common denominator.
Find the LCD for 5xy and 4y².
LCD = 20xy²
Rewrite equivalent fractions using the LCD.

16. Rewrite the variable expressions with a common denominator.
CHALLENGE
Rewrite the variable expressions with a common denominator.

17. Homework
Text page 190, #40-68 evens