Dozens

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
 
In the interactivity below, the computer generates two random digits.
Your task is to find the largest possible three-digit number which uses the computer's digits, and one of your own, to make a multiple of 2, 3, 4 or 6.

Can you decribe a strategy that ensures your first 'guess' is always correct?
 

Enter the biggest three-digit multiple of you can think of that uses the digits:
and



 1, 3, 4 and 5


Something else to think about:
 
What is the largest possible five-digit number
divisible by $12$ that you can make from the digits
$1$, $3$, $4$, $5$ and one more digit? 
 
Click here for a poster of this problem.