A large high altitude air shower observatory (LHAASO) located at Daocheng in Sichuan province, China, with an altitude up to 4410 m above the sea level, takes the function of hybrid technology to detect cosmic rays. It is composed of three sub-arrays: a 1.3 km ²ground-based particle detector array (KM2A) for γ-ray astronomy and cosmic ray physics, a 78000 m ²water Cherenkov detector array (WCDA) for γ-ray astronomy, and 18 wide field-of-view air Cherenkov/fluorescence telescopes array (WFCTA) for cosmic ray physics. As the major array of LHAASO, KM2A is composed of 5195 electromagnetic particle detectors (EDs, each with 1 m ²) and 1188 muon detectors (MDs, each with 36 m ²). In the ground-based experiments, there are two common independent data acquisition systems, corresponding to the shower and scaler operation modes. Up to now, the KM2A array operates only in shower mode with the primary energy threshold of about 10 TeV. In the scaler mode, it is not necessary for too many detectors to be hit at the same time. The energy threshold of the experiment can be greatly lowered. In order to learn more about the scaler mode in LHAASO-KM2A, we adopt the CORSIKA 7.5700 to study the cascade processes of extensive air showers in the atmosphere, and employ the G4KM2A (based on Geant4) to simulate the detector responses. The KM2A-ED array is divided into dozens of clusters. For one cluster (composed of 64 EDs), the event rates of showers having a number of fired EDs ≥ 1, 2, 3, 4 (in a time coincidence of 100 ns) are recorded. The average rates of the four multiplicities are ~88 kHz, ~1400 Hz, ~220 Hz, and ~110 Hz, respectively. The particle multiplicities m≥ 3 are almost completely due to cosmic ray secondary particles. The corresponding primary energies and effective areas are also given in this paper. According to our simulations, the energy threshold of the scaler mode can be lowered to 100 GeV, and the effective areas reach up to ~100 m ². The simulation results in this work are helpful in the online triggering with the scaler mode, and provide information for the subsequent data analysis in LHAASO-KM2A.