...the divisor problem. John told me a friend of his thought it could be 8,9. If this was so, the 'number' would be 4620, and the question states it is less than 4000. Here's why it isn't 8,9:

The LCM of 2 to 12 is 27720 (taking the highest powers of each prime factor). We can knock out 7 and 8 by dividing the LCM by 7 and then by 2, without affecting any of the other numbers. This leaves 27720 / 7 / 2 =1980, the solution (Sorry there was an error on the 'answer sheet' I posted!)

To remove 8 and 9 we would have to take out prime factors 2 and 3 from the LCM, giving 27720 / 2 / 3 = 4620 > 4000. Take out any more prime factors and you will eliminate more numbers from the divisors.

Hope this helps...if not wait for the next problem. It will be the Monty Hall problem as explained in The Curious Incident of the Dog in the Night-time.