The informal BRICS group (Brazil, Russia, India, China and South Africa) is actively working to solve the most acute global problems. This is why opportunities for implementing the sustainable development goals (SDGs) at BRICS summits is a topic for urgent research. This article discusses the prospects for achieving SDG 17.11 by the least developed countries (LDCs) in the framework of mutual trade with BRICS. SDG 17.11, unlike other goals, was expected to be achieved in 2020, but World Trade Organization (WTO) estimates for 2018 showed that progress was too slow. Against the sharp drop in international trade in 2020 due to economic shutdowns, the implementation of this goal is especially high on the agenda. This article describes the current implementation of the SDG by BRICS. A general analysis of mutual trade between LDCs and BRICS shows the low involvement of least developed countries in trade with BRICS. The methodology for the study involves computations of two trade indices and the identification of new clusters of LDCs. The export propensity index and trade intensity index are calculated in order to identify the countries with the most promise to increase exports to BRICS. The authors selected 13 LDCs with prospects for trade development with BRICS—Angola, Democratic Republic of the Congo, Mozambique, Bangladesh, Guinea, Mauritania, Nepal, Tanzania, Zambia, Bhutan, Lesotho, Malawi and Solomon Islands. Among 34 other LDCs, the authors identify five clusters based on their economic structure, including the role played in their economies by official development assistance (ODA) and personal remittances. Clustering allows BRICS to provide targeted support to LDCs in order to increase their export potential through the most effective mechanisms for each economy.