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LCM: Least Common Multiple

Learn about Least Common Multiple (LCM) and how to find it by listing multiples. A multiple is created by multiplying a number by counting numbers (1, 2, 3, ...). Understanding the difference between factors and multiples is crucial, as multiples are numerous while factors are limited. For example, the first five multiples of 4 are 4, 8, 12, 16, and 20. We demonstrate finding the LCM through examples with numbers like 12 and 18, concluding that the LCM of these is 36. Lastly, we show how to find the LCM of 9 and 10, which is 90.

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LCM: Least Common Multiple

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  1. LCM: Least Common Multiple

  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. • DON’T GET THEM CONFUSED WITH FACTORS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! • Factors are few but multiples are many. • Multiples are Mounting, it’s like skip counting!!!!

  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. Method #1:Find the LCM of the numbers by listing the multiples till you find a match • 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

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