What is the smallest positive integer, which has - for each of the digit 0-9 - a divisor ending with this digit?
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1 Answer
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It's
$270$, which has divisors $1, 2, 3, 54, 5, 6, 27, 18, 9, 10$.
Note that
the number must be a multiple of $10$
and then just
try every multiple of $10$ until it hits.
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$\begingroup$ Because 10 is coprime with with any number ending in 9 then you only need to check multiples of 90,190,290,... which significantly reduces the search space. $\endgroup$– hexominoApr 11, 2021 at 8:29
LCM(1, 2, ..., 9, 10) = 2520. $\endgroup$