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Least Common Multiple Warm Up Exercise 1. Joanne is campaigning for class president and plans to distribute some campaign materials: 20 flyers and 16 buttons. She wants each classroom to receive an identical set of campaign materials, without having any materials left over. What is the greatest number of classrooms Joanne can distribute materials to? 2. Serena wants to create snack bags for a trip she is going on. She has 6 granola bars and 10 pieces of dried fruit. If the snack bags should be identical without any food left over, what is the greatest number of snack bags Serena can make? Warm Up Exercise • Joanne is campaigning for class president and plans to distribute some campaign materials: 20 flyers and 16 buttons. She wants each classroom to receive an identical set of campaign materials, without having any materials left over. What is the greatest number of classrooms Joanne can distribute materials to? – 16 – 1, 2, 4, 8, 16 – 20 – 1, 2, 4, 5, 10, 20 GCF: 4 – Joanne can distribute campaign materials to 4 classrooms Warm Up Exercise • Serena wants to create snack bags for a trip she is going on. She has 6 granola bars and 10 pieces of dried fruit. If the snack bags should be identical without any food left over, what is the greatest number of snack bags Serena can make? – 6 – 1, 2, 3, 6 – 10 – 1, 2, 5, 10 GCF: 2 – Serena can make 2 snack bags of granola bars and dried fruit Lesson Objective • We can identify the least common multiple of two whole numbers Least Common Multiple (LCM) Vocabulary: Multiple – the product of any quantity and an integer. 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…List all the multiples of the number C…all terms in common M…from their list of multiples find the smallest Least Common Multiple (LCM) Important to Remember… THREE There are methods for finding the Common Multiples of two or more numbers… Method 1…Use Multiple Lists Method 2…Use Prime Factorization Method 3…Multiply the Numbers*** 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 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 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) 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 2. 2, 4, and 5 3. 4, 6, and 8 => 30 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 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 Least Common Multiple • Least Common Multiple Study Jams: http://studyjams.scholastic.com/studyjams/ja ms/math/fractions/least-commonmultiple.htm