x=nr cautat (cel mai mic)
x:12=c1 rest 8
x:10=c2 rest 6
x=?
D=C•Î+R
x=12c1+8 <=> x=12c1+12-4 <=> x+4=12(c1+1) => (x+4) divizibil cu 12
x=10c2+6 <=> x=10c2+10-4 <=> x+4=10(c2+1) => (x+4) divizibil cu 10
=> x+4=c.m.m.m.c. al nr. 12 si 10
12=2²•3
10=2•5
------------
c.m.m.m.c.=2²•3•5=4•3•5=3•20=60
x+4=60 <=> x=60-4 <=> x=56
Proba :
56:12=4 rest 8
56:10=5 rest 6
