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Least Common Multiple Chapter 5 Lesson 1 EQ: How do we find the LCM? Multiples A multiple is formed by multiplying a given number by the counting numbers. The counting numbers are 1, 2, 3, 4, 5, 6, etc. Example: List the multiples of 4: 4x1=4 4x2=8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24 Counting Numbers So, the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, etc. What are the first five multiples of 13? 13 x 1 =13 13 x 2 = 26 13 x 3 = 39 13 x 4 = 52 13 x 5 = 65 13, 26, 39, 52, 65 Find the Missing Multiples 6, 30 24 ____ 12, 18, ____, 3 ___, 15 ____, 18 21 6, 9, 12, ____, 12 ___, 72 24, 36, 48, 60, ____ Least Common Multiple (LCM) The least common multiple is the smallest number that is common between two lists of multiples. EXAMPLE: Find the LCM of 12 and 18 The multiples of 12: The multiples of 18: •12 x 1 = 12 •18 x 1 = 18 •12 x 2 =24 •18 x 2 = 36 •12 x 3 = 36 •18 x 3 = 54 •12 x 4 = 48 •18 x 4 = 72 •12 x 5 =60 •18 x 5 = 90 12, 24, 36, 48, 60 18, 36, 54, 72, 90 The first number you see in both lists is 36. The least common multiple of 12 and 18 is 36. Example 2: Find the LCM of 9 and 10 9, 18, 27, 36, 45, 54, 63, 72 81, 90, 99 10, 20, 30, 40, 50, 60, 70, 80 90, 100, 110 If you don’t see a common multiple, make each list go further. The LCM of 9 and 10 is 90 Example 3: Find the LCM of 4 and 12 4, 8, 12, 16 12, 24, 36 Answer: 12 Using Prime Factorization to find the LCM • Make factor trees for each number. Write the prime factorization in exponent form. •Identify all of the prime numbers among the prime factorizations. Every prime number will be used. • When the same prime number occurs in more than one prime factorization, select the prime that there’s more of (for example, 25 beats 22.) • Multiply your prime numbers to get the LCM. Example: Find the LCM of 88 and 102 88 102 2 x 44 2 x 51 2 x 22 2 x 11 88 = 23 x 11 102 = 2 x 3 x 17 LCM: 23 x 3 x 11 x 17 = 4,488 3 x 17 We have to use every prime number. The numbers we will use are 2, 3, 11, and 17. We have 2 in both places. Select the “bigger” one. 23 beats regular 2. Homework Time