Question

Determinati cel mai mare nr de 3 cifre care impartit la 12,16 si 18 da restul 10 ,14 si respectiv 16 si cum se rezolva

Answer 1

x:12=C(1) rest 10=>x=12C(1)+10|+2=> =>x+2=12*(C(1)+1)
x:16=C(2)rest 14=>x=16C(2)+14|+2=>
=>x+2=16*(C(2)+1)
x:18=C(3)rest 16=>x=18c(3)16|+2=>
=>x+2=18*(C(3)+1)

=>x+2 apratine M lui 12,16,18

[12,16,18](cel mai mic multiplu comun)
12=2^2*3
16=2^4
18=2*3^2
_____________
[12,16,18]=2^4*3^2=144=>x apartine M lui 144=> x={0*144,1*144,....} ,dar x =cel mai mare nr de trei cifre=> x=6*144=864