<s>[INST] Find the value of $n$ such that $(n-6)$ is divisible by $6$, $(n-7)$ is divisible by $7$ and $(n-8)$ is divisible by $8$. If $(n-6)$ is divisible by $6$, $(n-7)$ is divisible by $7$ and $(n-8)$ is divisible by $8$, then what is the value of $n $?
 [/INST] If $n - 6$ is divisible by $6$, then so is $n$. Likewise for $7$ and $8$; that is, $n$ is divisible by $6$, $7$ and $8$. There are infinitely many such values; the smallest positive value is the least common multiple of $6$, $7$ and $8$.
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