n : 24 = c₁ rest 19 ⇒ n = 24 × c₁ + 19 l + 5 ⇒ n + 5 = 24 × ( c₁ + 1 )
n : 30 = c₂ rest 25 ⇒ n = 30 × c₂ + 25 l + 5 ⇒n + 5 = 30 × ( c₂ + 1 )
n : 36 = c₃ rest 31 ⇒ n + 5 = 36 × ( c₃ + 1 )
___________________________________
⇒ n + 5 = c.m.m.m.c al numerelor 24; 30 si 36
____________________________________
24 = 2³ x 3
30 = 2 x 3 x 5
36 = 2² x 3²
___________________
c.m.m.m.c al numerelor ( 24; 30 si 36 ) = 2³ x 3² x 5 = 360
____________________________________________
n + 5 = 360 ⇒ n = 360 - 5 ⇒ n = 355
____________________________________
Verific:
355 : 24 = 14 rest 19
355 : 30 = 10 rest 25
355 : 36 = 9 rest 36
______________________________
Raspuns: 355 → numarul
