Question 7
Let $a, b, c, d, e$ be integers such that $1 \leq a \lt b \lt c \lt d \lt e$. Prove that
$$
\frac{1}{[a, b]} + \frac{1}{[b, c]} + \frac{1}{[c, d]} + \frac{1}{[d, e]} \leq \frac{15}{16}
$$
where $[m, n]$ denotes the least common multiple of $m$ and $n$ (e.g. $[4,6]=12$).
$$
\frac{1}{[a, b]} + \frac{1}{[b, c]} + \frac{1}{[c, d]} + \frac{1}{[d, e]} \leq \frac{15}{16}
$$
where $[m, n]$ denotes the least common multiple of $m$ and $n$ (e.g. $[4,6]=12$).