diff --git a/src/diffusers/schedulers/scheduling_lcm_flax.py b/src/diffusers/schedulers/scheduling_lcm_flax.py
index f45ca18ef190..51a8c0711eb3 100644
--- a/src/diffusers/schedulers/scheduling_lcm_flax.py
+++ b/src/diffusers/schedulers/scheduling_lcm_flax.py
@@ -2,8 +2,9 @@
 from dataclasses import dataclass
 from typing import List, Optional, Tuple, Union
 
-import flax
+import jax
 import jax.numpy as jnp
+import flax
 
 from ..configuration_utils import ConfigMixin, register_to_config
 from ..utils import BaseOutput, logging
@@ -341,17 +342,14 @@ def step(
         (step_index,) = jnp.where(state.timesteps == timestep, size=1)
         step_index = step_index[0]
 
-        # 1. get previous step value
+        # 1. get previous step value        
         prev_step_index = step_index + 1
-        if prev_step_index < len(state.timesteps):
-            prev_timestep = state.timesteps[prev_step_index]
-        else:
-            prev_timestep = timestep
+        prev_timestep = jax.lax.select(prev_step_index < len(state.timesteps), state.timesteps[prev_step_index], timestep)
 
         # 2. compute alphas, betas
-        alpha_prod_t = state.alphas_cumprod[timestep]
-        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
-
+        alpha_prod_t = state.common.alphas_cumprod[timestep]
+        alpha_prod_t_prev = jax.lax.select(prev_timestep >=0, state.common.alphas_cumprod[prev_timestep], state.final_alpha_cumprod)
+        
         beta_prod_t = 1 - alpha_prod_t
         beta_prod_t_prev = 1 - alpha_prod_t_prev
 
@@ -360,15 +358,14 @@ def step(
 
         # 4. Compute the predicted original sample x_0 based on the model parameterization
         if self.config.prediction_type == "epsilon":  # noise-prediction
-            predicted_original_sample = (sample - beta_prod_t.sqrt() * model_output) / alpha_prod_t.sqrt()
+            predicted_original_sample = (sample - jnp.sqrt(beta_prod_t) * model_output) / jnp.sqrt(alpha_prod_t)
         elif self.config.prediction_type == "sample":  # x-prediction
             predicted_original_sample = model_output
         elif self.config.prediction_type == "v_prediction":  # v-prediction
-            predicted_original_sample = alpha_prod_t.sqrt() * sample - beta_prod_t.sqrt() * model_output
+            predicted_original_sample = jnp.sqrt(alpha_prod_t) * sample - jnp.sqrt(beta_prod_t.sqrt) * model_output
         else:
             raise ValueError(
-                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` or"
-                " `v_prediction` for `LCMScheduler`."
+                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` or `v_prediction` for `LCMScheduler`."
             )
 
         # 5. Clip or threshold "predicted x_0"
@@ -400,7 +397,7 @@ def step(
         if not return_dict:
             return (prev_sample, state)
 
-        return FlaxLCMSchedulerOutput(prev_sample=prev_sample, denoised=denoised)
+        return FlaxLCMSchedulerOutput(prev_sample=prev_sample, state=state)
 
     # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.add_noise
     def add_noise(