When a natural number is divided by 3, the remainder is 2, when divided by 5, the remainder is 2, when divided by 7, the remainder is 5, when divided by 9, the remainder is 5, and when divided by 11, the remainder is 4. What is the smallest natural number that satisfies these conditions?
一个自然数除以3余2，除以5余2，除以7余5，除以9余5，除以11余4，则满足这些条件的最小自然数是多少？
<gadget id="calculator">3 * 5</gadget>
<output>15</output>

<gadget id="calculator">2 + 15</gadget>
<output>17</output>

<gadget id="calculator">15 * 2</gadget>
<output>30</output>

<gadget id="calculator">17 + 30</gadget>
<output>47</output>

<gadget id="calculator">105 * 2</gadget>
<output>210</output>

<gadget id="calculator">47 + 210</gadget>
<output>257</output>

<result>257</result>