Question

aflati cel mai mic numar natural care impartit la 6 da restul 5 si impartit la cinci da restul 4

Answer 1

X : 6 = a rest 5 ==> X = 6×a+5 |+1
X : 5 = b rest 4 ==> X = 5×b + 4 |+1

==> X + 1 = 6×(a+1)
==> X + 1 = 5×(b+1)

X + 1 = 6 × 5
X = 30 - 1 = 29 (numarul cautat)

29 : 6 = 4 rest 5
29 : 5 = 5 rest 4

Answer 2

Fie x = numarul cautat ( cel mai mic ) 

x:6=c1 rest 5 
x:5=c2 rest 4 

x=?

D=C*Î+R 

x=6c1+5 ⇒ x=6c1+6-1 ⇒ x+1=6(c1+1) ⇒ (x+1) divizibil cu 6
x=5c2+4 ⇒ x=5c2+5-1 ⇒ x+1=5(c2+1) ⇒ (x+1) divizibil cu 5
⇒ x+1=c.m.m.m.c. al numerelor 6 si 5

6=2*3
5=5 
--------
c.m.m.m.c.=2*3*5=30 

x+1=30 ⇔ x=30-1 ⇒ x=29