The multiples of
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$\,2\,$ are $\,2\,$, $\,4\,$, $\,6\,$, $\,8\,$, $\,10\,$, $\,12\,$, $\,14\,$, $\,16\,$, $\,18\,$, and so on.
Notice that the multiples of
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$\,2\,$ are obtained by taking the number $\,2\,$, and
multiplying successively by $\,1\,$, $\,2\,$, $\,3\,$, $\,\ldots\,$
Notice also that $\,2\,$ goes into each of these numbers evenly.
The multiples of
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$\,3\,$ are $\,3\,$, $\,6\,$, $\,9\,$, $\,12\,$, $\,15\,$, $\,18\,$, $\,21\,$, $\,24\,$, $\,27\,$, and so on.
Notice that the multiples of
[beautiful math coming... please be patient]
$\,3\,$ are obtained by taking the number $\,3\,$, and
multiplying successively by $\,1\,$, $\,2\,$, $\,3\,$, $\,\ldots\,$
Notice also that $\,3\,$ goes into each of these numbers evenly.
In general, the multiples of a number
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$\,\,x\,\,$ are
$\,\,x\,$, $\,\,2x\,$, $\,\,3x\,$, $\,\,4x\,$, and so on.
To test if something is a multiple of
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$\,\,x\,$, just see if $\,\,x\,\,$ goes into it evenly.