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Least Common Multiple

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This lesson focuses on the concept of multiples and the Least Common Multiple (LCM). A multiple is created by multiplying a given number by counting numbers like 1, 2, and 3. For example, the multiples of 4 are 4, 8, 12, and so on. We also explore how to find the first few multiples of a number, such as 13. The LCM is the smallest common multiple between two lists of multiples. The lesson includes examples to find the LCM of different pairs of numbers like 12 and 18, providing a thorough understanding of these mathematical concepts.

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Least Common Multiple

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  1. Least Common Multiple Lesson 3-6

  2. 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.

  3. Example: List the multiples of 4: • 4 x 1 = 4 • 4 x 2 = 8 • 4 x 3 = 12 • 4 x 4 = 16 • 4 x 5 = 20 • 4 x 6 = 24 So, the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, etc. Counting Numbers

  4. 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

  5. Find the Missing Multiples 24 30 • 6, 12, 18, ____, ____ • ___, 6, 9, 12, ____, ____, 21 • ___, 24, 36, 48, 60, ____ 3 15 18 72 12

  6. Least Common Multiple (LCM) • The least common multiple is the smallest number that is common between two lists of multiples.

  7. EXAMPLE: Find the LCM of 12 and 18 • The multiples of 12: • 12 x 1 = 12 • 12 x 2 =24 • 12 x 3 = 36 • 12 x 4 = 48 • 12 x 5 =60 • The multiples of 18: • 18 x 1 = 18 • 18 x 2 = 36 • 18 x 3 = 54 • 18 x 4 = 72 • 18 x 5 = 90

  8. 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.

  9. 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

  10. Example 3:Find the LCM of 4 and 12 4, 8, 12, 16 12, 24, 36 Answer: 12

  11. Example 5:Find the LCM of 6 and 20 6, 12, 18, 24, 30, 36 42, 48, 54, 60 20, 40, 60, 80, 100, 120 Answer: 60

  12. Homework Time

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