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Are you here?. Question:. If 5 is a factor of 35, what are all of the factors of 35? If 7 is a factor of 105, what are all of the factors of 105? What is the smallest factor that 35 and 105 share? What is the largest?. 2 2 • 3 2 = 2 • 2 • 3 • 3.

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  1. Are you here? Question: If 5 is a factor of 35, what are all of the factors of 35? If 7 is a factor of 105, what are all of the factors of 105? What is the smallest factor that 35 and 105 share? What is the largest?

  2. 22 • 32 = 2 • 2 • 3 • 3 • Use this to make an organized list of factors: 1 • 36; 2 • ____ 3 • ____ 4 (2•2) • ____ 6 (2•3) • ____ 9 (3•3) • ____ 12 (2•2•3) • ____ 18 (2•3•3) • ____ • Notice the duplication.

  3. Prime factorization for 72 = 23 • 32 • How can you make sure you get every factor? • 1, 2, 4, 8, 3, 9, 6, 12, 24, 18, 36, 72 • Try this one: 60 = 22 • 3 • 5 • 1, 2, 4, 3, 5, 6, 10, 15, 12, 20, 60 • Try this one: 48 = 24 • 3 • 1, 2, 4, 8, 16, 3, 6, 12, 24, 48

  4. Now, look at multiples • Suppose you have the number 20. • 20 = 22 • 5. A multiple will be found by taking any whole number and multiplying it by 20 (22 • 5). • So: 3 • 20 = 60 • So: 5 • 20 = 100 • So: 8 • 20 = 160.

  5. 2 • 60 2 • 42 2 • 30 2 • 21 2 • 15 3 • 7 3 • 5 Let’s look at 2 numbers • 120 84

  6. 120 = 2 • 2 • 2 • 3 • 584 = 2 • 2 • 3 • 7 • So, 120 = 23 • 3 • 5 and 84 = 22 • 3 • 7 • 120: factors are 1, 2, 4, 8, 3, 5, 6, 12, 24, 10, 20, 40, 15, 30, 60, 120 • 84: factors are 1, 2, 4, 3, 7, 6, 12, 14, 28, 42, 84 • To find their common factors, we see that they both have 1, 2, 4, 3, 6, and 12. The Greatest Common Factor is 12. • From the prime factorization: 2 • 2 • 3.

  7. 120 = 2 • 2 • 2 • 3 • 584 = 2 • 2 • 3 • 7 120 : 120, 240, 360, 480, 600, 720, 840, 960, 84 : 84, 168, 252, 336, 420, 504, 588, 672, 756, 840, 924, 1008 840 = 120 • 7 840 = 84 • 10

  8. 120 = 2 • 2 • 2 • 3 • 584 = 2 • 2 • 3 • 7 • Now: multiples of 120 will be 2 • 2 • 2 • 3 • 5 (or 120) multiplied by some other number. Multiples of 84 will be 2 • 2 • 3 • 7 (or 84) multiplied by some other number. Begin with the factors of the larger number. Think: the LCM will be 120 multiplied by some other number. Underline the factors of the smaller number. Fill in the missing factors. 120 •7= 840. 840 = 7 • 120 840 = 10 • 84 (10 is from 2 • 5)

  9. Let’s try another together • Find LCM of 38 and 95 38 = 2 • 19 95 = 5 • 19 LCM will be 38 multiplied by some number. LCM will be 95 multiplied by some number

  10. 38 : 76, 114, 152, 190, 228, 266, 304, 342, 380, 418, 456, 494, 532 • 95 : 95, 190, 285, 380, 475, 570, 665, 760, 855, 950 • 380 = 38 • 10 • 380 = 95 • 5

  11. Another way to look at it • 38 = 2 • 19 • 95 = 5 • 19 • LCM = 19 •(what) isa multiple of 38 but not a factor of 95. • 19

  12. Let’s try a few more • LCM of 28 and 140 • 126 = 2 • 3 • 3 • 7 • 140 = 2 • 2 • 5 • 7 • Think: both 140 and 126 are factors of the LCM. Start with either factor: • 126 (factors: a 2, two 3s, and a 7). From140, we still need a 2 and a 5. • LCM = 126 • 2 • 5 = 1260. • Check: 1260 = 140 • 3 • 3 = 1260

  13. Word Problem Example • Tara can run around the track in 5 minutes. Todd can run the same distance in 6 minutes, and Tony can do it in 8 minutes. If they start at the same time, when will they next meet at the starting line? • (Find the LCM of 5, 6, and 8) • Answer: 120 minutes or 2 hours

  14. Homework--due Wednesday and Friday next week • Turn in completed Exploration 4.2 with tables 1 & 2 and Sieve (see online for details) • Section 4.3 p. 252 #1d, 2a, 3d, 5, 7, 10, 11, 14, 17ab (see online for details)

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