Question

1.Aflati c.m.m.d.c.-ul si c.m.m.m.c.-ul pentru numerele de mai jos:
a) 18, 32, 64; b) 144, 320; c) 175, 200, 225; d) 576, 144; e) 169,195;

va rog ajutor dau coroana!!

Answer 1

Răspuns:

a) 18=3^2*2

32=2^5

64=2^6

cmmdc=2

cmmmc=3^2*2^6=9*64=576

b) 144=2^4*3^2

320=2^6*5

cmmdc= 2^4=16

cmmmc=2^6*5*3^2=64*5*9=2880

c) 175=5^2*7

200=2^3*5^2

225=5^2*3^2

cmmdc=5^2=25

cmmmc=5^2*7*2^3*3^2=25*7*8*9=12600

d)576=2^6*3^2

144=2^4*3^2

cmmdc=2^4*3^2=16*9=144

cmmmc=2^6*3^2=576

e)169=13^2

195=5*3*13

cmmdc=13

cmmmc=5*3*13^2=15*169=2535

Answer 2

$a)18 = 3 {}^{2} \times 2$

$32 = 2 {}^{5}$

$64 = 2 {}^{6}$

$cmmdc = 2$

$cmmmc = 3 {}^{2} \times 2 {}^{6} = 9 \times 64 = 576$

$b)144 = 2 {}^{4} \times 3 {}^{2}$

$320 = 2 {}^{6} \times 5$

$cmmdc = 2 {}^{4} = 16$

$cmmmc = {2}^{6} \times 5 \times 3 {}^{2} = 64 \times 5 \times 9 = 2880$

$c)175 = 5 {}^{2} \times 7$

$200 = {2}^{3} \times {5}^{2}$

$225 = {5}^{2} \times {3}^{2}$

$cmmdc = {5}^{2} = 25$

$cmmmc = {5}^{2} \times 7 \times 2 {}^{3} \times {3}^{2} = 25 \times 7 \times 8 \times 9 = 12600$

$d)576 = {2}^{6} \times {3}^{2}$

$144 = 2 {}^{4} \times 3 {}^{2}$

$cmmdc = 2 {}^{4} \times 3 {}^{2} = 16 \times 9 = 144$

$cmmmc = 2 {}^{6} \times 3 {}^{2} = 576$

$e)169 = {13}^{2}$

$195 = 5 \times 3 \times 13$

$cmmdc = 13$

$cmmmc = 5 \times 3 \times {13}^{2} = 15 \times 169 = 2535$

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