LCM of $n$ consecutive natural numbers Is there an efficient way to calculate the least common multiple of $n$ consecutive natural numbers? For example, suppose $a = 3$ and $b = 5$, and you need to find the LCM of $(3,4,5)$. Then the LCM of $3,4$ and $5$ is $60$. Is there an efficient way to do this for arbitrary $a$ and $b (a\leq b)$ that is more efficient than the naive approach$?$ 
Edit: What if I know the LCM of (1,2,3,4,..a) and the LCM of (1,2,3,..b). Is it possible to get the LCM of (a,a+1,..b) ?

A very interesting trick to find $LCM$,though its not exactly the same as your question.It does not deal with consecutive set of numbers.-
Let the numbers are-$(8,12).$
Steps:-
1.Find their $GCD$-Here it is $4.$
2.Now divide any of the given numbers by the $GCD$.Let us divide $8$ by $4$ here.It is equal to $2$.
3.Now,multiply it by the other number.Here it is $2*12=24$.It's your LCM.
