Question

stiind ca a si b sunt numere naturale astfel incat a x b=180 su c.m.m.m.c. [a, b]=30 aflati c.m.m.d.c. (a,b)

Answer 1

a·b=180;
⇒c.m.m.m.c[a,b]=30;
⇒a=30/x;
⇒b=30/y;
⇒30x/·30/y=180
⇒[30²]/x·y=180
⇒900/x·y=180
⇒x·y=900/180
⇒x·y=5;
⇒x,y∈[[1,5],[5,1]];
⇒a∈[6,30];
⇒b∈[6,30];
⇒a,b∈[[6,30],[30,6]];
⇒6=2·3⇒descompunere in factori primi;
⇒30=2·3·5;
⇒c.m.m.d.c=2·3=6;

Answer 2

[tex]a*b=180\\\\ c.m.m.m.c ~[a,b]=30\\\\ a= \frac{30}{x} \\\\ b= \frac{30}{y} \\\\ \frac{30}{x} * \frac{30}{y} =180\\\\ \frac{900}{x*y} =180\\\\ x*y= \frac{900}{180} \\\\ x*y=5\\\\ x,y\in[1;5];[5;1]\\\\ a\in[6;30]\\\\ b/in[6;30]\\\\ a,b\in[6;30]~;~[6;30]\\\\ cm.m.d.c.=2*3=6\\\\ ~~~~~~~~~~~~6=2*3\\ ~~~~~~~~~~~~30=2*3*5 [/tex]