Question

Aflati cel mai mic numar natural care impartit ,pe rand, la 240 , 600 si 840 da , resturile 204 , 564 , respectiv 804

Answer 1

a : 240 = x rest 204 => a=240x+204 |+36
a : 600 = y rest 564 =>a=600y+564 |+36
a : 840 = z rest 804 =>a=840z+804 |+36

==> a + 36 = 240(x+1)
==> a + 36 = 600(y+1)
==> a + 36 = 840( z+1)

240 = 2^4 × 3 × 5
600 = 2^3 × 3 × 5^2
840 = 2^3 × 3 × 5 × 7
_________________
c.m.m.m.c = 2^4 × 3 × 5^2 × 7 = 8400

a + 36 = 8400
a = 8400 - 36
a = 8364 (numarul cautat)