Circular Economy (CE) can help reduce the building industry's immense environmental impact. Life cycle assessment (LCA) can facilitate CE decision-making by identifying the largest environmental impact reduction opportunities throughout a building's life cycle, but it does not suffice in a design situation. Thus, aggregated LCA knowledge is needed. However, existing building LCAs lack transparency, coherence and a closer coupling with the building context. Performing in-depth systematic LCA on four Danish case-study buildings (a school, an office, a residential building and a hospital), this study identifies where the largest embodied greenhouse gas emissions (EG) exist. The study also identifies which building design and construction strategies should be in focus in transitioning the building sector to a CE. The LCA generalisations found that all the buildings exhibited considerable EG originating from production and replacement of floors and ceilings, outer walls, inner walls and roofs. Thus, to come closer to meeting climate goals, a combination of different strategies going across and beyond the life cycles of buildings, components and materials is needed. These strategies include reusing existing buildings, components and materials; avoiding, substituting or reducing the use of EG-intensive and short-lived materials; and enabling future reuse, recycling and/or energy recovery options for materials. Differences between the buildings were also found. Thus, it is suggested to combine generalised learnings with LCA of buildings on a case-to-case basis, and to focus on optimising EG-intensive components and materials based on their different use-contexts and interconnectedness rather than on optimising the entire building.