Repunits

The repunits are numbers with all their digits being 1 : 11, 111, 1111, etc.

We deal here with those which are multiple of a given number.

The smallest repunit which is a multiple of 3 is then 111 (obvious)

But what is the smallest repunit multiple of 13 ? Solution
multiple of 23 ? Solution
multiple of 123 ? Solution
Any general method ?

Details

 

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