Least possible upper and lower quartiles of a data set with a given interquartile range and no outliers

The members of a cycling club each recorded the time, in minutes, that they took to ride a hill route. The box-and-whisker diagram summarises these times; \(L\) is the lower quartile and \(U\) is the upper quartile.

For these times the interquartile range is \(16\) minutes, and none of the recorded times is an outlier.

1. Find the least possible value of \(U\).[3]
2. Hence, deduce the smallest value that \(L\) could take.[2]