Răspuns: 174
Explicație pas cu pas:
n : 12 = c₁ rest 6 ⇒ n = 12 × c₁ + 6 l + 6 ⇒ n + 6 = 12 × ( c₁ + 1)
n : 15 = c₂ rest 9 ⇒ n = 15 × c₂ + 9 l adun 6 ⇒ n + 6 = 15 × ( c₂ + 1 )
n : 18 = c₃ rest 12 ⇒ n = 18 × c₃ + 12 l + 6 ⇒ n + 6 = 18 × ( c₃ + 1 )
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⇒ n + 6 = c.m.m.m.c al numerelor 12; 15 si 18
12 = 2²× 3
15 = 3 × 5
18 = 2 × 3²
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c.m.m.m.c al numerelor = 2² x 3²x 5 = 180
⇒ n + 6 = 180 ⇒ n = 180 - 6 ⇒ n = 174 → numarul
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verific:
174 : 12 = 14 rest 6
174 : 15 = 11 rest 9
174 : 18 = 9 rest 12
