Question

aflati cel mai mic numar natural care impartit pe randa 24, 30,36 da respectivr resturile 19, 25 si 31 si caturile nenule
ajutoooooor va rov frumosss

Answer 1

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 )

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⇒  n + 5 = c.m.m.m.c al numerelor 24;  30 si 36

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24 = 2³ x 3

30 = 2 x 3 x 5

36 = 2² x 3²

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c.m.m.m.c al numerelor ( 24;  30  si 36 ) = 2³ x 3² x 5 = 360

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n + 5 = 360 ⇒   n = 360 - 5 ⇒   n = 355

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Verific:

355 : 24 = 14 rest 19

355 : 30 = 10 rest 25

355 : 36 =  9 rest 36

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Raspuns:   355 → numarul