Question

Să se afle cel mai mic numar natural care impartita numerele 2,3,5 da restul 1.

Answer 1

x:2=c1 rest 1
x=c1*2+1
x-1=c1*2
x-1=M2
x:3=c2 rest 1
x=c2*3+1
x-1=c2*3
x-1=M3
x:4=c3 rest 1
x=c3*4+1
x-1=c3*4
x-1=M4
x-1=M2=M3=M4
x-1=cmmmc(2;3;4)
2/2
1/
2=1*2
3/3
1/
3=1*3
4/2
2/2
1/
4=2^2
Se iau toti factorii primi la puterile cele mai mari.
cmmmc(2;3;4)=2^2*3=12
x-1=12
x=12+1
x=13