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### 3 6

1. 1. Least Common Multiple Lesson 3-6
2. 2. Multiples <ul><li>A multiple is formed by multiplying a given number by the counting numbers. </li></ul><ul><li>The counting numbers are 1, 2, 3, 4, 5, 6, etc. </li></ul>
3. 3. Example: List the multiples of 4: <ul><li>4 x 1 = 4 </li></ul><ul><li>4 x 2 = 8 </li></ul><ul><li>4 x 3 = 12 </li></ul><ul><li>4 x 4 = 16 </li></ul><ul><li>4 x 5 = 20 </li></ul><ul><li>4 x 6 = 24 </li></ul>Counting Numbers So, the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, etc.
4. 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. 5. Find the Missing Multiples <ul><li>6, 12, 18, ____, ____ </li></ul><ul><li>___, 6, 9, 12, ____, ____, 21 </li></ul><ul><li>___, 24, 36, 48, 60, ____ </li></ul>24 30 3 15 18 12 72
6. 6. Least Common Multiple (LCM) <ul><li>The least common multiple is the smallest number that is common between two lists of multiples. </li></ul>
7. 7. EXAMPLE: Find the LCM of 12 and 18 <ul><li>The multiples of 12: </li></ul><ul><li>12 x 1 = 12 </li></ul><ul><li>12 x 2 =24 </li></ul><ul><li>12 x 3 = 36 </li></ul><ul><li>12 x 4 = 48 </li></ul><ul><li>12 x 5 =60 </li></ul><ul><li>The multiples of 18: </li></ul><ul><li>18 x 1 = 18 </li></ul><ul><li>18 x 2 = 36 </li></ul><ul><li>18 x 3 = 54 </li></ul><ul><li>18 x 4 = 72 </li></ul><ul><li>18 x 5 = 90 </li></ul>
8. 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. 9. Example 2: Find the LCM of 9 and 10 9, 18, 27, 36, 45, 54, 63, 72 10, 20, 30, 40, 50, 60, 70, 80 If you don’t see a common multiple, make each list go further. 81, 90, 99 90, 100, 110 The LCM of 9 and 10 is 90
10. 10. Example 3: Find the LCM of 4 and 12 4, 8, 12, 16 12, 24, 36 Answer: 12
11. 11. Example 5: Find the LCM of 6 and 20 6, 12, 18, 24, 30, 36 20, 40, 60, 80, 100, 120 42, 48, 54, 60 Answer: 60
12. 12. Homework Time