Question

aflati cel mai mic numar natural care impartit la 8, 12, 15 da resturile 7, 11 si 14.

Answer 1

x = 8a + 7
x = 12b + 11
x = 15 c + 14

Descompunem in factori primi :
8 / 2^3
1
8 = 2^3

12 / 2^2
  3 / 3
  1
12 = 2^2 x 3^1

15 / 3
  5 / 5
  1
15 = 3^1 x 5^1

Aflam cmmmc
[ 8, 12, 15 ] = 2^3 x 3^1 x 5^1 = 8 x 3 x 5 = 24 x 5 = 120

x = 120 + 7
x = 127

Verificare :
127 : 8 = 15  rest 7
127 : 12 = 10  rest 7
127 : 15 = 8  rest 7