Question

determinati cel mai mic numar natural care impartit la numarul 24 da restul 10, si impartit la 36 da restul 22​

Answer 1

Răspuns:

x:24=c₁ r 10

x=24c₁ +10

x=24c₁+24-14

x=24c₁-14

x:36=c₂ r 22

x=36c₂ +22

x=36c₂+36-14

x=36c₂-14

24=2³·3

36=2²·3²

c.m.m.m.c (24;36)= 2³·3²=8·9=72

x+14=72=>x=72-14=58

Answer 2

Răspuns:  58

Explicație pas cu pas:

n : 24 = c₁ rest 10 ⇒    n = 24 × c₁ + 10   [ + 14 ⇒  n + 14 = 24 × ( c₁ + 1 )

n : 36 = c₂ rest 22 ⇒    n = 36 × c₂ + 22  [ + 14 ⇒  n + 14 = 36 × ( c₂ + 1 )

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n + 14 = c.m.m.m.c al numerelor 24 si 36

24 = 2³ × 3

36 = 2² × 3²

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c,m,m,m,c = 2³ × 3² = 72

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n + 14 = 72  ⇒   n = 72 - 14   ⇒   n = 58 → deimpartitul

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Verific:

58 : 24 = 2 rest 10

58 : 36 = 1 rest 22