:15 =c₁ rest 13 ⇒ a-13 =15×c₁
a:30=c₂ rest 13 ⇒ a-13=30×c₂
a:45=c₃ rest 13 ⇒ a-13=45×c₃
⇒ a - 13 = 15×c₁= 30×c₂ = 45×c₃
15 = 3×5
30=2×3×5
45=3²×5
__________
cmmmc (15, 30, 45) =2×3²×5=90
M₉₀= (180, 270, 360, 450, 540, 630, 720, 810, 900, )
a -13 =180 ⇒a=180+13=193 (deimpartitul)
Verific:
193 :15=12 rest 13
193 : 30= 6 rest 13
193 : 45=4 rest 13
Suma acestor numere este: (adaug la fiecare multiplu restul 13)
193 +(270+13) + (360+13) +(450+13)+(540+13) +(630+13)+(720+13)+(810+13)+(900+13)=
=193+283+373+463+553+643+733+823+913=
=4 977
