a:12 = x rest 9 ==> a =12x+9 |+3
a:16 = y rest 13 ==> a = 16y+13 |+3
a:20 = z rest 17 ==> a = 20z + 17 |+3
==> a +3 = 12×(x+1)
==> a+3 = 16×(y+1)
==> a+3 = 20×(z+1)
12 = 2^2 × 3
16 = 2^4
20 = 2^2 × 5
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c.m.m.m.c = 2^4 × 3 × 5 = 16×15 = 240
a + 3 = 240
a = 240 - 3 = 237 (numarul cautat)
Verificare:
237 : 12 = 19 rest 9
237 : 16 = 14 rest 13
237 : 20 = 11 rest 17
