7 itself. Actually, 0 is also divisible by 7, as are negative multiples of 7, so it really depends what set of numbers you consider. If you include negative numbers, there is no "smallest multiple".
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The smallest number that is divisible by the numbers 1 through 10, except 7 and 8, is 180.
7 is the smallest since it certainly divides into itself by 1, but if you mean the smallest number greater than 7 then the answer is 7 x 7 = 49.
7 is the smallest prime number which divides 539.
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There are an infinite number of them.126 is the smallest one.