Question

Determinati cel maimai mic numar natural care impartit pe rand la 24 48 40 da fiecare data restul 17 si caturi nenule

Answer 1

(restul=17)
numarul cautat este:
c.m.m.m.c (24,48,40)+17
24=2^3×3
48=2^4×3
40=2^3×5
c.m.m.m.c+17=2^4×3×5+17=240+17=257

Answer 2

n:24=x, rest 17 ⇒n=24x+17 ⇒ n-17=24x
n:48=y, rest 17 ⇒n=48y+17 ⇒ n-17=48y
n:40=z, rest 17 ⇒n=40z+17 ⇒ n-17=40z

Cautam c.m.m.m.c pentru numerele 24,48 si 40.

$24= 2^{3} *3$
$48= 2^{4} *3$
$40= 2^{3} *5$

$[24,48,40]= 2^{4}*3*5=240$

Avem:

n-17=240
n=240+17
n=257

Verificare:

257:24=10, rest 17
257:48=5, rest 17
257:40=6, rest 17

In concluzie, numarul cautat este 257.