What is the least integer greater than 1000 that is divisble by 6, 8, and 9? How to get the number fast? The answer is 1008
Trial and error is a good start. Prime factorization can work too. 6=23
8=2^3, 9=3^2.
So your multiples need to be of 72 because 2^23^3=72.
1008 is the first one.