Question

Determinati cel mai mic numar natural stiind ca imaprtit la 9 , 12, 18 da restul 8 de fiecare data.[

Answer 1

x:9=c1 rest 8  ⇒x= M₉ +8

x:12=c2 rest 8 ⇒x=M₁₂ +8

x:18=c3 rest 8  ⇒x=M₁₈ + 8

9=3²
12=2² * 3
18=3² * 3
[9;12;18]= 3² *2²= 9*4=36

x-cel mai mic
x=36+8=44

Answer 2

Folosesti teorema impartirii cu rest. D=I*C+r
x : 9 = a, r8 => x = 9a + 8 => x-8 = 9a => 9 | x-8
x : 12 = b, r8 => x = 12b + 8 => x-8 = 12b => 12 | x-8
x : 18 = c, r8 => x = 18c + 8 => x-8 = 18c => 18 | x-8
c.m.m.m.c [ 9, 12 18 ] = 36
Deci 36 = x-8 => x = 44