Question

Aflati cel mai mic numar natural care impartit la 8, 12 si 15 da resturile 7, 11 si 14.

Answer 1

X:8=C REST 7   ⇒ x=8c+7     ⇒x+1=8c+8
x:12=c rest 11    ⇒ x=12c+11 ⇒x+1=12c+12
x:15=c rest 14    ⇒x=15c+14  ⇒x+1=15c+14

x+1∈M[8,12,15]
8=2³
12=2²·3
15=5·3
[8,12,15]=2³·3·5=120
M120={120,240,360,480.....}
x+1=120
x=120-1
x=119
119:8=14 rest 7
119:12=9 rest 11
119:15=7 rest 14
deci cel mai mic nr.este 119