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We propose a simple method of characterizing the sensitivities of the cladding modes of an optical fiber to environmental conditions through the analysis of a single device. These sensitivities to conditions such as temperature, strain, and the refractive index of the surrounding medium are of particular relevance to the fabrication of long-period gratings (LPGs). The inferred sensitivities are all valid around the design wavelength of the analyzed fiber Bragg grating (FBG) device, and so can provide important design information for the manufacture of a LPG device that couples to a single or several cladding modes. To demonstrate the method, we use a FBG with a design wavelength of 1550 nm to determine the sensitivity of the cladding modes of a standard telecomm fiber to both temperature and strain. Using this information we infer the environmental sensitivity of any LPG fabricated in this fiber that operates around this wavelength. We design and fabricate LPGs to couple to selected cladding modes and measure the sensitivities of these devices directly. We find good agreement between the directly measured and inferred sensitivities.