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 
$$ {\rm lcm}\ (a,b,c) = {\rm lcm}\ (a,{\rm lcm}\ (b,c)).$$

It’s often useful to view $\operatorname{lcm}$ and $\gcd$ as $\max$ and $\min$, respectively, applied to the exponents of each prime in the prime factorizations. It’s clear that $\max$ and $\min$ are associative in the sense that
$$
\min(x,y,z)=\min(\min(x,y),z)=\min(x,\min(y,z))\;,
$$
and likewise for $\max$, and this transfers directly to $\operatorname{lcm}$ and $\gcd$.
