Question

Aflati cel mai mic numar natural care impartit la 8 si la 20 da restul 6 respectiv 18

Answer 1

n : 8 = c₁ rest 6 ⇒    n = 8 × c₁ + 6      l + 2 ⇒  n + 2 = 8 × ( c₁ + 1 )

n : 20 = c₂ rest 18 ⇒ n = 20 × c₂ + 18  l + 2 ⇒ n + 2 = 20 × ( c₂ + 1 )

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⇔  n + 2 = c.m.m.m.c al numerelor 8 si 20

8 = 2³

20 = 2² x 5

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c .m.m.m.c al numerelor ( 8 si 20 ) = 2³ x 5 = 40

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n + 2 = 40 ⇒  n = 40 - 2 ⇒  n = 38 → numarul natural

Verific:

38 : 8 = 4 rest 6

38 : 20 = 1 rest 18

Raspuns:    38 → numarul natural care, impartit la 8 si 20, da restul 6, respectiv 18