This work formulates a QUBO model for the closest string problem. It also provides an alternative QUBO model building on the notion that it is sometimes preferred to have stepwise functions eliminated from an optimization problem. The formulated QUBO models have been evaluated on a limited number of simple test cases using D-Wave quantum annealers. The range of values preferred for the Lagrange multipliers has been deduced, and the guidelines for choosing them, including the chain strength, have been discussed. Furthermore, the limitations of the D-Wave system w.r.t. the QUBO formulations devised are evaluated.