Wait, maybe

We can do this by knowing that

$lcm(a,b)*gcd(a,b)=a*b$ .

we get lcm(0,1)=\(\frac{0}{1} )=1

This can also be proved by a simple example:

$\frac{1}{0}+\frac{1}{1} \approx \frac{1}{0}$

LCM means least common $\text{multiple}$ .
All multiples of 0 are 0. But 0 is a multiple of every number. 0 is a multiple of every number. Here, $1×0=0$ So, their lcm is $\color{#69047E}{\boxed{0}}$ .