The non-zero natural number n is not only the sum of 2010 numbers and the same natural number, but also the sum of 2012 numbers and the same natural number, or the sum of 2013 numbers and the same natural number, so what is the smallest n?
不为零的自然数n既是2010个数字和相同的自然数之和，也是2012个数字和相同的自然数之和，还是2013个数字和相同的自然数之和，那么n最小是多少？
<gadget id="calculator">4 * 1_000</gadget>
<output>4_000</output>

<gadget id="calculator">3 * 10</gadget>
<output>30</output>

<gadget id="calculator">2_006 * 1</gadget>
<output>2_006</output>

<gadget id="calculator">4_000 + 30 + 2_006</gadget>
<output>6_036</output>

<result>6_036</result>