Question

Calculati c.m.m.d.c și c.m.m.m.c pentru numerele:a)15și35;b)48și72;c)120și360;d)420și350.Vă rog este urgent
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Answer 1

Răspuns:

$a)15 = 3 \times 5 \\ 35 = 5 \times 7 \\ c.m.m.d.c = 5 \\ c.m.m.m.c = 3 \times 5 \times 7 = 15 \times 7 = 105 \\ \\ b)48 = {2}^{4} \times 3 \\ 72 = {2}^{3} \times {3}^{2} \\ c.m.m.d.c = {2}^{3} \times 3 = 8 \times 3 = 24 \\ c.m.m.m.c = {2}^{4} \times {3}^{2} = 16 \times 9 = 144 \\ \\ c)120 = {2}^{3} \times 3 \times 5 \\ 360 = {2}^{3} \times {3}^{2} \times 5 \\ c.m.m.d.c = {2}^{3} \times 3 \times 5 = 8 \times 3 \times 5 = 24 \times 5 = 120 \\ c.m.m.m.c = {2}^{3} \times {3}^{2} \times 5 = 8 \times 9 \times 5 = 72 \times 5 = 360 \\ \\ d)420 = {2}^{2} \times 3 \times 5 \times 7 \\ 350 =2 \times {5}^{2} \times 7 \\ c.m.m.d.c = 2 \times 5 \times 7 = 10 \times 7 = 70 \\ c.m.m.m.c = {2}^{2} \times 3 \times {5}^{2} \times 7 = 4 \times 3 \times 25 \times 7 = 12 \times 25 \times 7 = 300 \times 7 = 2100$

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