Hi Alex,
I am going to do a similar problem.
Find the LCM of 231 and 294
First I would find the prime factorization of the two numbers
231 = 3 7 11
294 = 2 3 7^{2}
If N is a multiple of 231 then the prime factorization of N must contain at least one 3, one 7 and one 11. If N is also a multiple of 294 then the prime factorization of N must contain at least one 2, at least one 3 and at least two 7's. Thus the smallest such N is
N = 2 3 7^{2} 11
This is the LCM of 231 and 294.
Penny
