If $n$ and $k$ are positive integers such that $5<\frac nk<6$, then what is the smallest possible value of $\frac{\mathop{\text{lcm}}[n, k]}{\gcd(n, k)}$

Kayla wants to find the width, ab, of a river. she walks along the edge of the river 65 ft and marks point c. then she walks 25 ft further and marks point d. she turns 90° and walks until her location, point a, and point c are collinear. she marks point e at this location, as shown. (a) can kayla conclude that δ and δ are similar? why or why not? (b) suppose de = 15 ft. what can kayla conclude about the width of the river?