Question

calculati c.m.m.d.c al urmatoarelor grupe de numere a) 50;75 b) 32;48 c) 72;108 d)66;242 e)112;126 f)50;42;36 g)150;75;225 h)98;42;105

Answer 1

Pentru a afla c.m.m.d.c se scrie numarul in produs de factori primi iar apoi se iau factorii comuni cu cel mai mic exponent

a) 50;75

50 = 2 * $5^{2}$

75 = 3 *  $5^{2}$

=> c.m.m.d.c = $5^{2}$ = 25

b) 32;48

32 = $2^{5}$

48 = $2^{4}$ * 3

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

c) 72;108

72 = $2^{3}$ * $3^{2}$

108 = $2^{2}$ * $3^{2}$

d) 66;242

66 = 2*3*11

242 = $11^{2}$ * 2

cmmdc = 11 * 2 = 22

e) 112; 126

112 = $2^{4}$ * 7

126 = 2 * $3^{2}$ * 7

cmmdc = 7 * 2 = 14

f) 50;42;36

50 = $5^{2}$ * 2

42 = 2 * 7  * 3

36 = $2^{2}$ * $3^{2}$

cmmdc = 2

g) 150; 75;225

150 = 2*$5^{2}$ * 3

75 = 3* $5^{2}$

225 = $5^{2}$ * $3^{2}$

cmmdc = 75

h) 98; 42; 105

98 = $7^{2}$ * 2

42 = 2 * 7 * 3

105 = 5 * 7 * 3

cmmdc = 7