Question

Aflati cel mai mic numar natural care impartit pe rand la numerele 12,18 si 20 da,de fiecare data ,restul 5

Answer 1

n:12=c1,rest 5 n:18=c2,rest5 n:20=c3,rest5 n:12=c1,rest5=>n=12*c1+5|-5=>n-5=12*c1 n:18=c2,rest5=>n=18*c2+5|-5=>n-5=18*c2 n:20=c3,rest5=≥n=20*c3+5|-5=>n-5=20*c3 A=B*C n-5=12*c1=(n-5) divizibil cu 12 n-5=18*c2=(n-5) divizibil cu 18 n-5= 20*c3=(n-5) divizibil cu 20 (n-5) -> multiplu comun al nr 12,18, si 20 Deci: Calculam c.m.m.m.c [12,18,20] = 12= 2²*3} 18= 3²*2} => [12,18,20] = 3²*2*5*2=90 20= 2²* 5} Răspuns: 90