  We show that if a divisor centered over a point on a smooth surface computes
a minimal log discrepancy, then the divisor also computes a log canonical
threshold. To prove the result, we study the asymptotic log canonical threshold
of the graded sequence of ideals associated to a divisor over a variety. We
systematically study this invariant and also prove a result describing which
divisors compute asymptotic log canonical thresholds.
