Wednesday, October 13 (Blue) Thursday, October 14 (Gold) 1. Fill in planner (Practice 5-1) 2. Bell Work (Write the prime factorization of each number)

Objective

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

Vocabulary Multiple least common multiple (LCM) least common denominator (LCD)

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

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.

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.

3: 3, 6, 9, 12, 15, 18, 21, . . .

Find the smallest number that is in all the lists.

LCM: 21. In 21 days, both teams will have game on the same day again.

Remember!

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

Example 2: Find the LCM of 16 and 36

16 = 2 4 36 = 2 2 • 3 2 2 4 • 3 2 16 • 9 = 144 LCM: 144

Write the prime factorizations Use the greatest power of each factor. Multiply.

Example 3: Find the LCM of 5a 4 and 15a

5a 4 = 5 • a 4 15a = 3• 5 •a 3 • 5• a 4 15a 4 LCM: 15a 4

Write the prime factorizations Use the greatest power of each factor. Multiply.

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

12 48 60 20 45 56

m

4 60 180 75

xy

2

> 1 6 5 , 12 , 2 3 < < 1 5 3 , 10 , 1 2 7 , 12

Additional Example 2D: Using Multiples to Find the LCM Find the least common multiple (LCM).

15, 6, and 4

15 = 3 • 5 6 = 3 • 2

Write the prime factorization of each number in exponential form.

4 = 2 2 3 • 5 • 2 2 3 • 5 • 2 2 = 60 LCM: 60

To find the LCM, multiply each prime factor once with the greatest exponent used in any of the prime factorizations.

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.

0 1 2 3 4 5 6 The least common multiple (LCM) of 2 and 3 is 6.

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, … 9: 9, 18, 27, 36, 45, . . .

Find the smallest number that is in all the lists.

The least common multiple of 3, 4, and 9 is 36.

Check It Out: Example 2C Find the least common multiple (LCM).

Method 3: Use prime factorization.

4 and 10

4 = 2 • 2 10 = 2 • 5 2 • 2 • 5 2 • 2 • 5 = 20 LCM: 20

Write the prime factorization of each number. Line up the common factors. To find the LCM, multiply one number from each column.

Check It Out: Example 2D Find the least common multiple (LCM).

12, 6, and 8

12 = 2 2 • 3 6 = 2 • 3 8 = 2 3 2 3 • 3 2 3 • 3 = 24 LCM: 24

Write the prime factorization of each number in exponential form. To find the LCM, multiply each prime factor once with the greatest exponent used in any of the prime factorizations.

Lesson Quiz Find the least common multiple (LCM).

1. 6, 14 42 2. 9, 12 36 3. 5, 6, 10 30 4. 12, 16, 24, 36 144 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?

36 cm