Răspuns: 414
Explicație pas cu pas:
n : 14 = c₁ rest 8 ⇒ n = 14×c₁+8 l +6 ⇔ n+6= 14×c₁+14 ⇔ n+6 = 14×(c₁+1)
n : 15 = c₂ rest 9 ⇒ n = 15×c₂+9 l +6 ⇔ n+6 = 15×(c₂+1)
n : 60 = c₃ rest 54 ⇒ n = 60×c₃+54 l +6 ⇔ n+6=60×(c₃+1)
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n + 6 = [14; 15; 60]
14 = 2×7
15 = 3×5
60 = 2²×3×5
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c.m.m.m.c al nr. 14, 15, 60 = 2²×3×5×7 = 420
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n + 6 = 420
n = 420 - 6
n = 414 → numărul căutat
Verific:
414 : 14 = 29 rest 8
414 : 15 = 27 rest 9
414 : 60 = 6 rest 54
