There exist a formula to easily find the least common multiple of 2 integers:
$$ \operatorname{lcm}(x,y)=\frac {x\cdot y}{\gcd(x,y)} $$
And for multiple numbers:
$$ \operatorname{lcm}(a_1, a_2, \ldots ,a_n)=\frac {a_1\cdots a_n}{\gcd(a_1, a_2, \ldots ,a_n)} $$
I need help proving the latter by induction relying on the former formula.