Least Common Multiple (LCM)

Least Common Multiple (LCM) Essential Question: How do I find the least common multiple of two or three numbers, and why is this relevant to me? Common Core Objective: 6.NS.4 Students will be able to identify the least common multiple of two or three one, two, and three digit numbers with 80% accuracy.

Least Common Multiple (LCM) Vocabulary: Multiple – a non-zero . Least Common Multiple – the least non-zero common multiple of two or more numbers.

Least Common Multiple (LCM) When thinking about finding the Least Common Multiple, or the LCM… REMEMBER L…The smallest number C…all terms in common M…from their list of multiples

Least Common Multiple (LCM) Important to Remember… There are TWO methods for finding the Common Multiples of two or more numbers… Method 1…Use Multiple Lists Method 2…Use Prime Factorization

Least Common Multiple (LCM) Finding the LCM: Method 1 – Multiple List Example 1: Find the LCM of 4 and 9. Step 1: Create a list of multiples for each number Step 2: Circle the first multiple the numbers have in common 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, … 9: 9, 18, 27, 36, 45, 54, 63,… The LCM of 4 and 9 is 36

Least Common Multiple (LCM) Finding the LCM: Method 2 – Prime Factorization Example 1: Find the LCM of 4 and 9. Step 1: Find the prime factorization of each number. Step 2: Find the product of all the prime factors. 4 9 4: 2 · 2 9: 3 · 3 2 2 3 3 2 · 2 3 · 3 2 · 2 · 3 · 3 = 36 LCM = 36

Least Common Multiple (LCM) Finding the LCM: Method 3 – Find the Product Example 1: Find the LCM of 4 and 9. Step 1: For any two numbers, multiply them together Step 2: Your answer is the LCM of the numbers

Least Common Multiple (LCM) Finding the LCM: Method 3 – Find the Product Example 1: Find the LCM of 4 and 9. Step 1: For any two numbers, multiply them together Step 2: Your answer is the LCM of the numbers 4 x 9 LCM = 36 36

Least Common Multiple (LCM) Finding the LCM: Method 1 – Multiple List Example 2: Find the LCM of 10 and 12. Step 1: Create a list of multiple for each number Step 2: Circle the first multiple the numbers have in common 10: 10, 20, 30, 40, 50, 60, 70, 80,… 12: 12, 24, 36, 48, 60, 72, 84,… The LCM of 10 and 12 is 60

Least Common Multiple (LCM) Finding the LCM: Method 2 – Prime Factorization Example 2: Find the LCM of 10 and 12. Step 1: Find the prime factorization of each number. Step 1: Find the prime factorization of each number. Step 2: Find the product of all the prime factors

Least Common Multiple (LCM) Finding the LCM: Method 2 – Prime Factorization Example 2: Find the LCM of 10 and 12. Step 1: Find the prime factorization of each number. Step 1: Find the prime factorization of each number. Step 2: Find the product of all the prime factors 10 12 10: 2 · 5 12: 2 2 · 3 2 5 3 4 2 2 2 · 5 2 · 5 · 2 · 3 = 60 3 · 2 · 2 LCM = 60

Least Common Multiple (LCM) Finding the LCM: Method 1 – Multiple List Example 3: Find the LCM of 12 and 16. Step 1: Create a list of multiple for each number Step 2: Circle the first multiple the numbers have in common

Least Common Multiple (LCM) Finding the LCM: Method 1 – Multiple List Example 3: Find the LCM of 12 and 16. Step 1: Create a list of multiple for each number Step 2: Circle the first multiple the numbers have in common 12: 12, 24, 36, 48, 60, 72, 84, 96, … 16: 16, 32, 48, 64, 80, 96,… FYI…there is always more than one multiple for any set of numbers The LCM of 12 and 16 is 48

Least Common Multiple (LCM) Finding the LCM: Method 2 – Prime Factorization Example 3: Find the LCM of 12 and 16. Step 1: Find the prime factorization of each number. Step 1: Find the prime factorization of each number. Step 2: Find the product of all the prime factors 12 16 12: 2 · 2 · 3 16: 2 · 2 · 2 · 2 3 4 4 4 2 · 2 · 2 · 2 · 3 = 48 2 2 2 2 2 2 3 · 2 · 2 2 · 2 · 2 · 2 LCM = 48

Least Common Multiple (LCM) Important to Remember… There are TWO methods for finding the Common Multiples of two or more numbers… Method 1…Use Multiple Lists Method 2…Use Prime Factorization

Least Common Multiple (LCM) Guided Practice Problems Directions: Find the LCM for each number set. 1. 9 and 12 2. 4, 8, and 12 3. 2, 3, 6, and 8

Least Common Multiple (LCM) Guided Practice Problems Directions: Find the LCM for each number set. 1. 9 and 12 => 6 2. 4, 8, and 12 => 16 3. 2, 3, 6, and 8 => 24

Least Common Multiple (LCM) Independent Practice Problems Directions: Find the LCM for each number set. 1. 6 and 10 2. 2, 4, and 5 3. 4, 6, and 8

Least Common Multiple (LCM) Independent Practice Problems Directions: Find the LCM for each number set. 1. 6 and 10 => 30 2. 2, 4, and 5 => 20 3. 4, 6, and 8 => 24