Bo'linuvchanlik. Sonning natural bo'luvchilar soni va yig'indisi bo‘yicha savol

1‑dan 300 gacha bo‘lgan sonlar ichida $4$, $6$ va $10$ ga bir vaqtda bo‘linadigan sonlarni topamiz. Bunday son $ \operatorname{LCM}(4,6,10)$ ga bo‘linadi. $4=2^{2}$, $6=2\cdot3$, $10=2\cdot5$ ⇒ $\operatorname{LCM}=2^{2}\cdot3\cdot5=60$. Endi $1\le n\le300$ bo‘lsa $n$ ning $60$ ga bo‘linishi kerak, ya’ni $n=60k$ va $k$ natural son. $60k\le300 \Rightarrow k\le5$, shuning uchun $k=1,2,3,4,5$. Demak, $60,120,180,240,300$ sonlari shartni qanoatlantiradi – jami $5$ ta. Javob: **D) 5**.