1. Least Common Multiple (LCM)

2. Essential Question: How do I find the least common multiple of two or three numbers, and why is this relevant to me? Learning Target I can identify the least common multiple of two or three (one, two, and three) digit numbers with 80% accuracy. Least Common Multiple (LCM)

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

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

5. 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)

6. 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, … The LCM of 4 and 9 is 36 Least Common Multiple (LCM) 9: 9, 18, 27, 36, 45, 54, 63,…

7. 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. 49 LCM = 36 2 2 · 2 2 4: 2 · 2 9: 3 · 3 2 · 2 · 3 · 3 = 36 Least Common Multiple (LCM) 3 3 · 3 3

8. Finding the LCM: Method 1 – Multiple List Example 2: Find the LCM of 10 and 12. Least Common Multiple (LCM) 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,… The LCM of 10 and 12 is 60 12: 12, 24, 36, 48, 60, 72, 84,…

9. 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. Least Common Multiple (LCM) Step 1: Find the prime factorization of each number. Step 2: Find the product of all the prime factors

10. 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. Least Common Multiple (LCM) Step 1: Find the prime factorization of each number. Step 2: Find the product of all the prime factors 1012 LCM = 60 2 2 · 5 5 10: 2 · 5 12: 2 2 · 3 2 · 5 · 2 · 3 = 60 3 3 · 2 · 2 4 22

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

12. Finding the LCM: Method 1 – Multiple List Example 3: Find the LCM of 12 and 16. Least Common Multiple (LCM) Step 1: Create a list of multiple for each number Step 2: Circle the first multiple the numbers have in common The LCM of 12 and 16 is 48 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

13. Finding the LCM: Method 2 – Prime Factorization Example 3: Find the LCM of 12 and 16. Least Common Multiple (LCM) Step 1: Find the prime factorization of each number. Step 2: Find the product of all the prime factors 16 12 LCM = 48 2 2 · 2 · 2 · 2 2 12: 2 · 2 · 3 16: 2 · 2 · 2 · 2 2 · 2 · 2 · 2 · 3 = 48 3 3 · 2 · 2 4 22 22 4 4

14. 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)

15. 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)

16. Guided Practice Problems Directions: Find the LCM for each number set. 1. 9 and 12=> 36 2. 4, 8, and 12=> 24 3. 2, 3, 6, and 8=> 24 Least Common Multiple (LCM)

17. 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)

18. 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 Least Common Multiple (LCM)