Brainteaser (from Simont?)

[jack]

Do all numbers have a multiple which you can write (in base 10) solely with 0s and 1s?

Spoiler in the comments. And probably maths.

Comments

[khoth.livejournal.com]

There is a shorter way, although I'm not sure what it is. 143*7 = 1001.

[jack]

I don't there to normally be a convenient formula that species a *minimum* multiple, (even though there's a better solution in the comments on LJ than my solution). Am I missing something?