Answer
$LCM (a,b)=a\cdot b$ when $a$ and $b$ are relatively prime
Work Step by Step
When two numbers are relatively prime, their prime factorizations consist of distinct prime factors. Since there are no common factors between them, the $LCM$ is equals to their product.
For example, in the case of $6$ and $7$, the prime factorization of $6$ is $2\cdot 3$, and the prime factorization of $7$ is $7$. Since $6$ and $7$ have no common prime factors, their $LCM$ is equal to their product: $6\cdot 7 = 42$.
In general, if two numbers $A$ and $B$ are relatively prime, their $LCM$ is given by:
$LCM(A, B) = A \cdot B$
This is because the $LCM$ is the smallest positive integer that is divisible by both $A$ and $B$, and when there are no common factors, the smallest integer that satisfies this condition is their product.
