# Divisors ending with digits 0-9 each

What is the smallest positive integer, which has - for each of the digit 0-9 - a divisor ending with this digit?

• LCM(1, 2, ..., 9, 10) = 2520 . Apr 10 at 22:31

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.

• 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. Apr 11 at 8:29