1. Course 1 5-1 Least Common Multiple

2. Course 1 5-1 Least Common Multiple A multiple of a number is the product of the number and any nonzero whole number. Remember!

3. Course 1 5-1 Least Common Multiple 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)

4. Course 1 5-1 Least Common Multiple Additional Example 1: Consumer Application English muffins come in packs of 8, and eggs come in cartons of 12. If there are 24 students, what is the least number of packs and cartons needed so that each student has a muffin sandwich with one egg and there are no muffins left over? There are 24 English muffins and 24 eggs. So 3 packs of English muffins and 2 cartons of eggs are needed. Draw muffins in groups of 8. Draw eggs in groups of 12. Stop when you have drawn the same number of each.

5. Course 1 5-1 Least Common Multiple Check It Out: Example 1 There are 18 dog cookies and 18 bones. So 3 packages of dog cookies and 2 bags of bones are needed. Dog cookies come in packages of 6, and bones in bags of 9. If there are 18 dogs, what is the least number of packages and bags needed so that each dog has a treat box with one bone and one cookie and there are no bones or cookies left over? Draw cookies in groups of 6. Draw bones in groups of 9. Stop when you have drawn the same number of each.

6. Course 1 5-1 Least Common Multiple The smallest number that is a multiple of two or more numbers is the least common multiple (LCM).

7. Course 1 5-1 Least Common Multiple Additional Example 2A: Using Multiples to Find the LCM Find the least common multiple (LCM). Method 1: Use a number line. 3 and 4 Use a number line to skip count by 3 and 4. 0 2 4 6 8 10 12 The least common multiple (LCM) of 3 and 4 is 12.

8. Course 1 5-1 Least Common Multiple Additional Example 2B: Using Multiples to Find the LCM Find the least common multiple (LCM). Method 2: Use a list. 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44,... 5: 5, 10, 15, 20, 25, 30, 35, 40, 45,... 8: 8, 16, 24, 32, 40, 48,... LCM: 40 List multiples of 4, 5, and 8. Find the smallest number that is in all the lists. 4, 5, and 8

9. Course 1 5-1 Least Common Multiple 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.

10. Course 1 5-1 Least Common Multiple 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,... 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, … 9: 9, 18, 27, 36, 45,... The least common multiple of 3, 4, and 9 is 36. List multiples of 3, 4, and 9. Find the smallest number that is in all the lists.

11. Course 1 5-1 Least Common Multiple 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,…

12. Course 1 5-1 Least Common Multiple 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

13. Course 1 5-1 Least Common Multiple 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)

14. Course 1 5-1 Least Common Multiple 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,…

15. Course 1 5-1 Least Common Multiple 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

16. Course 1 5-1 Least Common Multiple 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)

17. Course 1 5-1 Least Common Multiple Lesson Quiz Find the least common multiple (LCM). 1. 6, 14 2. 9, 12 3. 5, 6, 104. 12, 16, 24, 36 4236 30 144