The LCT (log canonical thresholds) is an invariant which measures the complexity of singularities. A conjecture due to Shokurov predicts that LCT for a single divisor satisfy the ACC (ascending chain condition), and it was proven by Hacon-McKernan-Xu.In this talk, I will sketch the proof of the ACC of LCT polytopes (for multiple divisors). This is a joint work with Zhan Li and Lu Qi.