Question

Calcule o M.M.C e M.D.C de:
a)12,15
b)4,6,10
c)20,30
d)15,20,25
e)50,100
f)100,200,300
g)3,5,7

Answer 1

Calcule o M.M.C e M.D.C de:

mdc : máximo divisor comum

(divide todos ao mesmo tempo)

mmc : "mínimo múltiplo comum"

a)12,15

R.':

"Mdc = "3"

mmc = 60"

12,15 :2'

6,15:2'

3,15: 3(*)

1,5:5'

"1,1"

MmC = 2².3.5=4.15= "60"

mdc = "3"

_____________

b)4,6,10

R.:

mdc = "2"

mmc = "60"

4,6,10: 2(*)

2,3,5:2'

1,3,5: 3'

1,1,5:5'

"1,1,1"

mdc = "2"

mmc = 2².3.5= 4.15= '60'

________________

c)20,30

mdc = "10"

mmc = "60"

20,30: 2(*)

10,15: 2'

5,15: 3'

5,5: 5(*")

"1,1"

mdc= "10"

mmc = 2.2.3.5= 4.15= "60"

_____________

d)15,20,25

"Mdc ="5"

"mmc= 300"

15,20,25: 2'

15,10,25: 2'

15,5,25: 3'

5,5,25: 5: (*)"

"1,1,5':5'

"1,1,1"

" = "5"

MmC = 2.2.3.5.5 = "300"

____________

e)50,100"

R.:mdc

"Mdc = "50"

"mmc = "100"

50,100: 2(*)

25,50:: 2

25,25: 5(*)

5,5: 5(*)

'1,1'

mdc = 2.5²= 2.25= "50"

mmc = 2².5²= 4.25= "100"

_____________

f)100,200,300

100,200,300: 2(*)

50,100,150: 2(*)

25,50,75: 2'

25,25,75: 3'

25,25,25: 5(*)

5,5,5:5(*)

1,1,1'

Mdc = 2².5²= 100

mmc = 2³.3.5²= 8.3.25= "600"

R.:

Mdc = "100"

mmc = "600"

______________

g)3,5,7

mdc= "1"

mmc = "105"

3,5,7: 3'

1,5,7:5'

1,1, 7: 7'

--------------

= 3.5.7

= 15.7

= 105

____________