Răspuns:
A) 12=2^2×3
18=2×3^2
40=2^3×5
c. m. m. m.c =3^2×3^2×5=8×9×5=360
360 +7=367 ( cel mai mic număr natural care respecta condițiile cerinței)
367:12=30 rest 7
367:18=20 rest 7
367:40=9 rest 7
B) n:12=c1, rest 11=>n=12xc1 +11 1+1=>n +1=12x(c1+1)
n:18=c2 rest 17=>n=18×c2+17 1+1=>n +1 =18×(c2+1)
n:40=c3 rest 39=>n=40xc3+39 1+1 =>n+1=40x(c3+1)
22=2^2x3
18=2×3^2
40=2^3x5
c. m. m. m. c al numerelor (23, 18 și 40) =2^3×3^2x5=360
n+1=360=>n=360x 1=>n=359>
numărul
Verific :
359:12=29 rest 11
359:18=29 rest 17
359:40=8 rest 39
