Question

Determinati cel mai mic numar natural care impartit la 24 48 si 40 pe rand da de fiecare data restul 17

Answer 1

X(minim)-17 = M₂₄=M₄₈=M₄₀ = [24;48;40] = 240
 ↓↓
x(minim) = 240+17 = 257

Answer 2

x:24=c1 rest 17
x=c1*24+17
x-17=c1*24
x:48=c2 rest 17
x=c2*48+17
x-17=c2*48
x:40=c3 rest 17
x=c3*40+17
x-17=c3*40
x-17=cmmmc(24;48;40)
24/2
12/2
6/3
2/2
1/
24=2^3*3
48/2
24/2
12/2
6/2
3/3
1/
48=2^4*3
40/5
8/2
4/2
2/2
1/
40=2^3*5
Se iau toti factorii primi la puterile cele mai mari.
cmmmc(24;48;40)=2^4*3*5=240
x-17=240
x=240+17
x=257