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LLMs have been shown to perform well in machine translation (MT) with the use of in-context learning, rivalling supervised models when translating into high-resource languages (HRLs). However, they lag behind when dealing with low-resource language (LRLs). Example selection via similarity search and supervised fine-tuning help. However the improvements they give are limited by the size, quality and diversity of existing parallel datasets. A common technique in low-resource MT is synthetic parallel data creation, the most frequent of which is backtranslation, whereby existing target-side texts are automatically translated into the source language. However, it also relies on the existence of good quality and relevant target-side texts, which are not readily available for many LRLs. In this paper, we present a new approach, TopXGen, which involves using an LLM to automatically generate topic-specific target-side data in the LRL, which can then be backtranslated to produce useful and diverse parallel texts for ICL and fine-tuning. Our intuition is that while LLMs struggle to translate into LRLs, their ability to translate well into HRLs and their multilinguality enable them to generate good quality, natural-sounding target-side texts, which can be translated well into a high-resource source language. We show that TopXGen boosts LLM translation performance during fine-tuning and in-context learning. Our code and outputs will be made freely available.