This paper introduces a novel framework that leverages large language models (LLMs) for machine translation (MT). We start with one conjecture: an ideal translation should contain complete and accurate information for a strong enough LLM to recover the original sentence. We generate multiple translation candidates from a source language A to a target language B, and subsequently translate these candidates back to the original language A. By evaluating the cycle consistency between the original and back-translated sentences using metrics such as token-level precision and accuracy, we implicitly estimate the translation quality in language B, without knowing its ground-truth. This also helps to evaluate the LLM translation capability, only with monolingual corpora. For each source sentence, we identify the translation candidate with optimal cycle consistency with the original sentence as the final answer. Our experiments demonstrate that larger LLMs, or the same LLM with more forward passes during inference, exhibit increased cycle consistency, aligning with the LLM model size scaling law and test-time computation scaling law. This work provide methods for, 1) to implicitly evaluate translation quality of a sentence in the target language, 2), to evaluate capability of LLM for any-to-any-language translation, and 3), how to generate a better translation for a specific LLM.