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**Wednesday, October 13 (Blue) Thursday, October 14 (Gold)**

Fill in planner (Practice 5-1) Bell Work (Write the prime factorization of each number)

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Objective SWBAT find the Least Common Multiple (LCM) and compare and order fractions.

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**Vocabulary Multiple least common multiple (LCM)**

least common denominator (LCD)

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**A multiple of a number is the product of the number and any nonzero whole number.**

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**least common multiple (LCM): The smallest number that is a multiple of two or more numbers.**

least common denominator (LCD): The smallest number that is the multiple of two or more denominators.

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**Today, the school’s baseball and soccer teams had games**

Today, the school’s baseball and soccer teams had games. The baseball team plays every 7 days. The soccer team plays every 3 days. When will the teams have games on the same day again? 3,7 7: 7, 14, 21 , 28, 35, 42, List multiples of 3 and 7. Find the smallest number that is in all the lists. 3: 3, 6, 9, 12, 15, 18, 21, . . . LCM: 21. In 21 days, both teams will have game on the same day again.

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**The prime factorization of a number is the number written as a product of its prime factors.**

Remember!

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**Example 2: Find the LCM of 16 and 36**

16 = 24 Write the prime factorizations 36 = 22• 32 Use the greatest power of each factor. 24 • 32 Multiply. 16 • 9 = 144 LCM: 144

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**Example 3: Find the LCM of 5a4 and 15a**

Write the prime factorizations 15a = 3• 5 •a Use the greatest power of each factor. 3 • 5• a4 Multiply. 15a4 LCM: 15a4

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negative positive 7 7 7 -7 7 7 21 21 84 21 84 84 28 56 28 84 < < < < <

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**Additional Example 2D: Using Multiples to Find the LCM**

Find the least common multiple (LCM). 15, 6, and 4 15 = 3 • 5 Write the prime factorization of each number in exponential form. 6 = 3 • 2 4 = To find the LCM, multiply each prime factor once with the greatest exponent used in any of the prime factorizations. 3 • 5 • 22 3 • 5 • 22 = 60 LCM: 60

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**Find the least common multiple (LCM). Method 1: Use a number line. **

Check It Out: Example 2A Find the least common multiple (LCM). Method 1: Use a number line. 2 and 3 Use a number line to skip count by 2 and 3. The least common multiple (LCM) of 2 and 3 is 6.

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**Find the least common multiple (LCM). Method 2: Use a list. **

Check It Out: Example 2B Find the least common multiple (LCM). Method 2: Use a list. 3, 4, and 9 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, . . . List multiples of 3, 4, and 9. 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, … Find the smallest number that is in all the lists. 9: 9, 18, 27, 36, 45, . . . The least common multiple of 3, 4, and 9 is 36.

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**Find the least common multiple (LCM). **

Check It Out: Example 2C Find the least common multiple (LCM). Method 3: Use prime factorization. 4 and 10 4 = 2 • 2 Write the prime factorization of each number. 10 = • 5 Line up the common factors. 2 • 2 • 5 To find the LCM, multiply one number from each column. 2 • 2 • 5 = 20 LCM: 20

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**Find the least common multiple (LCM).**

Check It Out: Example 2D Find the least common multiple (LCM). 12, 6, and 8 12 = 22 • 3 Write the prime factorization of each number in exponential form. 6 = 2 • 3 8 = 23 To find the LCM, multiply each prime factor once with the greatest exponent used in any of the prime factorizations. 23 • 3 23 • 3 = 24 LCM: 24

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Lesson Quiz Find the least common multiple (LCM). 1. 6, , 12 3. 5, 6, , 16, 24, 36 5. Two students in Mrs. Albring’s preschool class are stacking blocks, one on top of the other. Reece’s blocks are 4 cm high and Maddy’s blocks are 9 cm high. How tall will their stacks be when they are the same height for the first time? 42 36 30 144 36 cm

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