Crushing is one of the most energy-consuming technological processes. The purpose of grinding is to achieve the desired grain size of mineral raw materials. The process of grinding consists of many factors, for example, the size and form of crushed grains, as well as their mutual arrangement inside the crushing machine chamber, the technological parameters of the crusher, the material properties, and the speed of the moving grains. One of the key parameters of the aggregate is its resistance to grinding. Resistance to grinding is related to the strength of the products made from aggregates subjected to grinding, which affects the overall quality of these products. Therefore, the aim of this study is to analyze the impact of the crushing of natural aggregate on the LA crumbling strength index. Two types of aggregates were analyzed—natural gravel and natural pebbles crushed in a crusher. Aggregates were acquired from two mines belonging to the plant Kruszgeo S.A. in Rzeszów, i.e., ZEK (Zakład Eksploatacji Kruszywa) Ostrów and ZEK Strzegocice II. The aggregate crushing process was carried out for 4–8 mm and 10–14 mm fractions using cone crushers of the 1044 type. Aggregate crushing was carried out in a Los Angeles drum, in accordance with the requirements of EN 1097-2:2020. The analysis showed that for grits of the 10–14 mm fraction, the lower values of the LA indices were obtained, which allows for obtaining a bigger index of crushing strength than in the case of crushing using the 4–8 mm fraction. This analysis showed how important the process of grinding aggregates is and, thus, the appropriate selection of fractions for the grit crushing process for the aggregate strength on grinding. Subjecting the aggregate to the grinding process results in an improvement in the crushing strength indicator, thus obtaining better strength parameters of the products manufactured from the aggregates subjected to the process of crushing (for example, concrete). The originality of the study is an analysis of key Polish aggregates and the crushing strength index.