Least Common Multiple Objective: To find the least common multiple Vocabulary: Least Common Multiple (LCM): The least non-zero common multiple of two or more numbers. Method 1: Make a list of multiples Ex: Find the LCM of 4 and 9 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44 4: 9: 9, 18, 27, 36, 45, 36 is the LCM of 4 and 9

Method 2: Prime factorization with factor trees. Find the LCM of 10 and 12 10 12 4 2 2 3 5 2 10 = 2 • 5 Multiply the factors, using the common factors only once 12 = 2•2•3 2•2•3•5 = 60

Method 3: prime factorization using upside-down division Find the LCM of 12 and 16 2 12 2 16 2 6 2 8 3 2 4 2 12 = 16 = 2•2 • 3 Multiply the factors using the common factors only once. 2•2•2•2 2•2•2•2•3= 48

Find the LCM of 24 and 84 24 84 2 2 12 42 6 7 No more common factors 2•2•6•7 = 168

88 180 120 225 Find the LCM of the following 1) 8 and 22 2) 18 and 20

       

You are having a barbeque and will be serving hot dogs You are having a barbeque and will be serving hot dogs. You notice that hot dogs are sold in packs of 6 and hot dog buns are sold in packs of 8. You want to have the same number of hot dogs as buns without any left over. How many packs of each should you buy? Hot Dogs: 6: 6, 12, 18, 24, 30, 36 HD Buns: 8: 8, 16, 24, 32,40 4 packs of Hot Dogs 3 packs of Buns