I know that the identity of this operator is 1, but am not sure about the inverse.
2026-02-23 03:28:33.1771817313
Which integers have inverses with respect to lcm operator, a*b=lcm (a,b)
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What does it mean to say that $m$ is the inverse of $n$ with respect to that operation? It means that $\operatorname{lcm}(m,n)=1$. So, your question becomes:
Can you take it from here?