Question

3) Determine pela decomposição simultânea, o mmc e o mdc de: a) 18, 27 e 45. b) 18, 30 e 48. c) 120, 132 e 20. d) 150, 300 e 375.

Answer 1

Resposta:

a) 18, 27, 48 | 2 MMC = 2⁴ . 3³ = 432

9, 27, 24 | 2 MDC = 3

9, 27, 12 | 2

9, 27, 6 | 2

9, 27, 3 | 3

3, 9, 1 | 3

1, 3, 1 | 3

1, 1, 1

b) 18, 30, 48 | 2 MMC = 2⁴ . 3² . 5 = 720

9, 15, 24 | 2 MDC = 2 . 3 = 3

9, 15, 12 | 2

9, 15, 6 | 2

9, 15, 3 | 3

3, 5, 1 | 3

1, 5, 1 | 5

1, 1, 1

c) 120, 132, 20 | 2 MMC= 2³ . 3 . 5 . 11 = 1320

60, 66, 10 | 2 MDC = 2² = 4

30, 33, 5 | 2

15, 33, 5 | 3

5, 11, 5 | 5

1, 11, 1 | 11

1, 1, 1

d) 150, 300, 375 | 2 MMC= 2² . 3 . 5³ = 1500

75, 150, 375 | 2 MDC= 3 . 5² = 75

75, 75, 375 | 3

25, 25, 125 | 5

5, 5, 25 | 5

1, 1, 5 | 5

1, 1, 1