A method to find out LCM(least common multiple) for a list of numbers I found a recursive formula to find out LCM(least common multiple) of 3 or more numbers in a website.I checked it and it works but I can not understand it fully.Can anyone tell me what is the reasoning behind the formula with better and clear explanation. The recursive formula is 
$$ {\rm lcm}\ (a,b,c) = {\rm lcm}\ (a,{\rm lcm}\ (b,c)).$$

Recall the Fact : $$ A|X,\ B|X \Rightarrow {\rm lcm}\ (A,B)|X $$
 Let $$ T:={\rm lcm}\ (a,b,c),\ S:={\rm lcm}\ (b,c) $$
$$b|T,\ c|T \Rightarrow S|T $$
And $$a|T\Rightarrow {\rm lcm}\ (a,S) | T $$
$$ b|S,\ c|S \Rightarrow b|{\rm lcm}\ (a,S),\ c|{\rm lcm}\ (a,S)
$$
And $$a|{\rm lcm}\ (a,S) \Rightarrow T|{\rm lcm}\ (a,S) $$
