Question

cum aflu: cel mai mic nr naturalcare: impartit la 6 are rest 4.impartit la 8 rest 6.impartit la 9 rest 7.catul este nenul.multumesc mult

Answer 1

n : 6 = c₁ rest 4 ⇒  n = 6 × c₁ + 4   l + 2  ⇒  n + 2 = 6 × ( c₁ + 1 )

n : 8 = c₂ rest 6 ⇒ n = 8 × c₂ + 6    l + 2 ⇒  n + 2 = 8 × ( c₂ + 1 )

n : 9 = c₃ rest 7 ⇒ n = 9 × c₃ + 7    l + 2 ⇒ n + 2 = 9 × ( c₃ + 1 )

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⇒  n + 2 = c.m.m.m.c. al numerelor ( 6;  8  si 9 )

6 = 2 × 3

8 = 2³

9 = 3²

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c.m.m.m.c. al numerelor ( 6;  8;  9 ) = 2³ × 3² = 72

⇔  n + 2 = 72 ⇒  n = 72 - 2 ⇒ n = 70 → numarul natural

Verific

70 : 6 = 11 rest 4

70 : 8 = 8 rest 6

70 : 9 = 7 rest 7

Raspuns:     70 →  cel mai mic nr natural