Recently, the integer DCT (Int-DCT), which has the rounding operations in the lifting structure, is attracting many researchers' attention as an effective method for DCT based lossy / lossless unified coding. So far, focuses of the previous reports relevant to the Int-DCT have been limited to a few topics such as how to reduce the number of multipliers with the four point lossless Hadamard transform and the non-separable two dimensional LDCT, What seems to be lacking, however, is how to express multipliers' word length as short as possible for reduction of hardware complexity. This report defines a new "SNR sensitivity" as an indicator of how the word length truncation of multiplier coefficients affects quality of the decoded image, and also proposes a new word length allocation method based on the sensitivity. As a result, two [bit] in average shorter word length is attained under equivalent quality of the decoded image.