Question

Determinati cel mai mic nr nat care impartit la 24 48 40 da de fiecare data caturi nenule di rest 17

Answer 1

   
$Notatie: \\ n = numarul cautat. \\ \\ Rezolvare: \\ n = cmmmc [24; 48; 40] + 17 \\ Descompunem numerele: \\ 24=2^3\cdot 3 \\ 48=2^4\cdot 3 \\ 40=2^3\cdot 5 \\ cmmmc = 2^4\cdot3\cdot5 = 16\cdot3\cdot5=48\cdot5 = 240 \\ n = cmmmc [24; 48; 40] + 17 = 240+17=257 \\ \\ Verificare: \\ 257 : 24 = 10 ~rest~17 \\ 257 : 48 = 5 ~rest~17 \\ 257 : 40 = 6 ~rest~17$