GCD to LCM of multiple numbers If I know the GCD of 20 numbers, and know the 20 numbers, is there a formula such that I input the 20 numbers and input their GCD, and it outputs their LCM? I know that
$$\frac{\left| a\cdot b\right|}{\gcd(a,b)} = \text{lcm}(a,b).$$
So is it$$\frac{\left| a\cdot b\cdot c\cdot d\cdot e\cdot f\right|}{\gcd(a,b,c,d,e,f)}?$$If not, what is it?
There can be no formula that computes $\text{lcm}(a,b,c)$ using only the values of $abc$ and $\gcd(a,b,c)$ as input: that's because $(a,b,c) = (1,2,2)$ and $(a,b,c) = (1,1,4)$ both have $abc=4$, $\gcd(a,b,c)=1$, but they don't have the same lcm.  

However, there is a straightforward generalization of the $2$-variable formula. For instance,
$$\text{lcm}(a,b,c,d) = \frac{abcd}{\gcd(abc,abd,acd,bcd)}.$$

The correct gcd to take is not of the individual terms $a,b,c,d$ but the products of all the complementary terms (which looks the same in the two-variable case).
LCM can be calculated using:
$\text{GCD}(a,b)\cdot \text{LCM}(a,b)=ab$ and
$\text{LCM}(a,b,c,d,...n)=\text{LCM}(\text{LCM}(a,b),c,d,...,n)$

Example
$\text{LCM}(2,4,5,7)=\text{LCM}(4,5,7)=\text{LCM}(20,7)=140$

or more concisely
$$
\begin{align}
2&amp;,4,5,7 \\
4&amp;,5,7 \\
20&amp;,7 \\
140&amp;
\end{align}
$$

http://mathhelpforum.com/peer-math-review/229498-lcm-b-c-abc.html