Răspuns: 359 => numarul
Explicație pas cu pas:
n : 12 = c₁ rest 11 => n = 12 x c₁ + 11 l + 1 => n + 1 = 12 x ( c₁ + 1 )
n : 18 = c₂ rest 17 => n = 18 x c₂ +17 l + 1 => n + 1 = 18 x ( c₂ + 1 )
n : 40 = c₃ rest 39 => n = 40 x c₃ + 39 l + 1 => n + 1 = 40 x ( c₃ + 1 )
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=> n + 1 = c.m.m.m.c al numerelor 12; 18 si 40
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12 = 2² x 3
18 = 2 x 3²
40 = 2³ x 5
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c.m.m.m.c. al numerelor ( 12; 18 si 40 ) = 2³ x 3² x 5 = 360
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n + 1 = 360 ⇒ n = 360 - 1 ⇒ n = 359 → numarul
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Verific:
359 : 12 = 29 rest 11
359 : 18 = 19 rest 17
359 : 40 = 8 rest 39
