Question

12) Calcular o mínimo múltiplo comum(mmc) dos números abaixo:
a) 6 e 8
b) 4e 9
c) 14 e 20
d) 12, 15 e 18
e) 15, 24 e 60​

Answer 1

Explicação passo-a-passo:

6, 8 | 2

3, 4 | 2

3, 2 | 2

3, 1 | 3

1, 1 | 1

MMC = 2 . 2 . 2 . 3 = 24

4, 9 | 2

2, 9 | 2

1, 9 | 3

1, 3 | 3

1, 1 | 1

MMC = 2 . 2 . 3 . 3 = 36

14, 20 | 2

7, 10 | 2

7, 5 | 5

7, 1 | 7

1, 1 | 1

MMC = 2 . 2 . 5 . 7 = 140

12,15,18/2

6,15,9/2

3,15,9/3

1,5,3/3

1,5,1/5

1,1,1

2²×3²×5=180

15,24,60/2

15,12,30/2

15,6,15/2

15,3,15/3

5,1,5/5

1,1,1

2³×3×5=120

Answer 2

$\boxed{\red{\begin{array}{lr}\bf MMC\to Minimo~m\acute{u}ltiplo~comum\end{array}}}$

$\red{\diamondsuit}$ Para calcularmos o MMC dos números da questão devemos fazer a decomposição simultânea dos números

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$\bf Quest\tilde{a}o~A$

$\large\begin{array}{r|l}6,8&2\\3,4&2\\3,2&2\\3,1&3\\1,1\end{array}$

$\large\boxed{\red{\sf 2^{3}\cdot 3=24}}$

$\bf Quest\tilde{a}o~B$

$\large\begin{array}{r|l}4,9&2\\2,9&2\\1,9&3\\1,3&3\\1,1\end{array}$

$\large\boxed{\red{\sf 2^{2}\cdot 3^{2}=36}}$

$\bf Quest\tilde{a}o~C$

$\large\begin{array}{r|l}14,20&2\\7,10&2\\7,5&5\\7,1&7\\1,1\end{array}$

$\large\boxed{\red{\sf 2^{2}\cdot 5\cdot 7=140}}$

$\bf Quest\tilde{a}o~D$

$\large\begin{array}{r|l}12,15,18&2\\6,15,9&2\\3,15,9&3\\1,5,3&3\\1,5,1&5\\1,1,1\end{array}$

$\large\boxed{\red{\sf 2^{2}\cdot 3^{2}\cdot 5=180}}$

$\bf Quest\tilde{a}o~E$

$\large\begin{array}{r|l}15,24,60&2\\15,12,30&2\\15,6,15&2\\15,3,15&3\\5,1,5&5\\1,1,1\end{array}$

$\large\boxed{\red{\sf 2^{3}\cdot 3\cdot 5=120}}$

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Espero ter ajudado e bons estudos!!!