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Cognitive impairment is a common complaint in people with multiple sclerosis (pwMS). The study objective was to determine the psychometric properties of the letter digit substitution test (LDST) that measures information processing speed and to investigate the impact of relevant predictors of LDST achievement in pwMS. The design was cross-sectional. The study included 87 pwMS and 154 control subjects. The validity of LDST was examined, and a hierarchical regression model was used to explore relevant predictors of LDST success. The LDST had excellent construct validity, as expressed by differences between pwMS and control subjects. Convergent validity of the LDST was supported by a significant moderate correlation with the expanded disability status scale (EDSS) (ρ = −0.36; p < 0.05) and a significantly strong correlation with the multiple sclerosis impact scale (MSIS-29) physical subscale (r = −0.64; p < 0.01). The LDTS score well differentiated the pwMS considering age, education, EDSS, disease duration, comorbidity, and medication therapy. Using the LDST as a criterion variable in pwMS results showed consistent evidence for the age, education, and EDSS impact on LDST performance. The best cut-off score of ≤35 discriminated the control and MS group. LDST proved to be a valid test for assessing information processing speed in pwMS.