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**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

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**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

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Objective SWBAT find the least common multiple of two numbers.

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**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.

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**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.

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**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.

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**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.

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**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

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**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.

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**“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. = = =

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**Compare the Following Fractions**

< > <

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**Order the fractions from least to greatest.**

Find the LCD for 4, 9, & 15. LCD = 180 Rewrite equivalent fractions using the LCD.

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**Order the fractions from least to greatest.**

Find the LCD for 6, 9, & 3. LCD = 18 Rewrite equivalent fractions using the LCD.

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**Rewrite the variable expressions with a common denominator.**

Find the LCD for 5b and 4ab². LCD = 20ab² Rewrite equivalent fractions using the LCD.

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**Rewrite the variable expressions with a common denominator.**

Find the LCD for 5xy and 4y². LCD = 20xy² Rewrite equivalent fractions using the LCD.

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**Rewrite the variable expressions with a common denominator.**

CHALLENGE Rewrite the variable expressions with a common denominator.

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Homework Text page 190, #40-68 evens

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