6.1.6 Least Common Multiple (LCM)

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Presentation transcript:

6.1.6 Least Common Multiple (LCM)

Vocabulary Common Multiples – Products that two factors have in common Example: 20 is a common multiple of 2 and 5 16 is a common multiple of 4 and 8 Least Common Multiple (LCM) is the smallest product two factors have in common Example: 10 is the least common multiple of 2 and 5 8 is the least common multiple of 4 and 8 Two options for finding the Least Common Multiple (LCM): 1. List multiples 2. Prime Factors

Find the LCM Using Lists of Multiples Find the LCM of 4 and 6 Step #1: List the multiples for 4 = 4, 8, 12, 16, 20, 24, 28, 36, 40 Step #2: List the multiples for 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 Step #3: Circle the multiples each factor has in common = 12, 24, 36 Step #4: Identify the smallest of these multiples = 12 The least common multiple (LCM) of 4 and 6 is 12.

Your Turn! Multiples Lists Find the LCM for the following factors using the multiples lists methods: 3, 8 9, 12 6, 10

Find the LCM Using Prime Factorization Find the LCM of 16 and 20 Step #1: Make a factor tree for each number Step #2: Write out the prime factorization for each number 16 = 2 x 2 x 2 x 2 20 = 2 x 2 x 5 Step #3: Look at the first prime factor for the first product and count how many times that factor appears in that prime factorization 2 shows up four times in the prime factorization of 16

Find the LCM Using Prime Factorization, Cont’d Step #4: Look at the other prime factorization and count how many times that same factor shows up in that prime factorization. 2 shows up twice in the prime factorization of 20 Step #5: Write out the factor where it appears the greater number of times. 2 x 2 x 2 x 2 Step #6: Repeat steps 3-5 for each factor. 5 shows up once in the prime factorization of 20, but not at all for 16. Step #7: Multiply all of the selected prime factors 2 x 2 x 2 x 2 x 5 = 80 The least common multiple of 16 and 20 is 80.

Your Turn! Prime Factorization Use prime factorization to find the LCM of the numbers below: 14, 18 28, 36 24, 90

HOmework Page 40 (#1, 2, 4, 5, 6, 8, 10, 12, 14, 16, 18)