Question

1. Calcule.
a) mmc (50, 75)
b) mmc (60, 24
c) mme (28, 48)
d) mme (10.1 À 45).
e) mmc (6.8. 12. 15)
f) mmc (12, 18, 36, 40)​

Answer 1

Resposta:

a) 

50, 75 | 2

25, 75 | 3

25, 25 | 5

    5, 5 | 5                                         

    1, 1 | 2 * 3 * 5² = 6 * 25 = 150

b) 

60, 24 | 2

30, 12 | 2

  15, 6 | 2

  15, 3 | 3

    5, 3 | 3

    5, 1 | 5                                              

    1, 1 | 2³ * 3² * 5 = 8 * 9 * 5 = 360

c)

28, 48 | 2

14, 24 | 2

  7, 12 | 2

    7, 6 | 2

    7, 3 | 3

    7, 1 | 7                                           

    1, 1 | 2⁴ * 3 * 7 = 16 * 21 = 336

d)

10, 12, 45 | 2

    5, 6, 45 | 2

    5, 3, 45 | 3

    5, 1, 15 | 3

      5, 1, 5 | 5                                               

      1, 1, 1 | 2² * 3² * 5 = 4 * 9 * 5 = 180

  

e)

6, 8, 12, 15 | 2

  3, 4, 6, 15 | 2

  3, 2, 3, 15 | 2

  3, 1, 3, 15 | 3

    1, 1, 1, 5 | 5                                           

    1, 1, 1, 1 | 2³ * 3 * 5 = 8 * 15 = 120

f)

12, 18, 36, 40 | 2

    6, 9, 18, 20 | 2

      3, 9, 9, 10 | 2

        3, 9, 9, 5 | 3

        1, 3, 3, 5 | 3

        1, 1, 1, 5 | 5                                              

        1, 1, 1, 1 | 2³ * 3² * 5 = 8 * 9 * 5 = 360

Answer 2

Resposta:

Explicação passo-a-passo:

$\begin{array}{rr|c|c} & & MMC & MDC \\50, & 75 & 2\\ 25, & 75 & 3\\ 25, & 25 & 5 & 5\\ 5, & 5 & 5 & 5\\ 1, & 1\\ \end{array}\\ MMC\,\,\ 2 \cdot 3 \cdot 5^2 = 150\\ MDC\,\,\ 5^2 = 25$

$\begin{array}{rr|c|c} & & MMC & MDC \\60, & 24 & 2 & 2\\ 30, & 12 & 2 & 2\\ 15, & 6 & 2\\ 15, & 3 & 3 & 3\\ 5, & 1 & 5\\ 1, & 1\\ \end{array}\\ MMC\,\,\ 2^3 \cdot 3 \cdot 5 = 120\\ MDC\,\,\ 2^2 \cdot 3 = 12$

$\begin{array}{rr|c|c} & & MMC & MDC \\28, & 48 & 2 & 2\\ 14, & 24 & 2 & 2\\ 7, & 12 & 2\\ 7, & 6 & 2\\ 7, & 3 & 3\\ 7, & 1 & 7\\ 1, & 1\\ \end{array}\\ MMC\,\,\ 2^4 \cdot 3 \cdot 7 = 336\\ MDC\,\,\ 2^2 = 4$

$\begin{array}{rrrr|c} & & & & MMC\\6, & 8, & 12, & 15 & 2\\ 3, & 4, & 6, & 15 & 2\\ 3, & 2, & 3, & 15 & 2\\ 3, & 1, & 3, & 15 & 3\\ 1, & 1, & 1, & 5 & 5\\ 1, & 1, & 1, & 1\\ \end{array}\\ MMC\,\,\ 2^3 \cdot 3 \cdot 5 = 120$

$\begin{array}{rrrr|c|c} & & & & MMC & MDC \\12, & 18, & 36, & 40 & 2 & 2\\ 6, & 9, & 18, & 20 & 2\\ 3, & 9, & 9, & 10 & 2\\ 3, & 9, & 9, & 5 & 3\\ 1, & 3, & 3, & 5 & 3\\ 1, & 1, & 1, & 5 & 5\\ 1, & 1, & 1, & 1\\ \end{array}\\ MMC\,\,\ 2^3 \cdot 3^2 \cdot 5 = 360\\ MDC\,\,\ 2 = 2$