What computer guided both the Apollo command and lunar modules?

The Apollo Guidance Computer guided both the Apollo command and lunar modules.

Developed for NASA by the MIT Instrumentation Laboratory, the AGC supplied guidance, navigation and control calculations during Apollo missions. It interfaced with the spacecraft’s inertial measurement system, optical equipment, radar and crew controls, helping the vehicles determine and maintain their flight paths.

Apollo lunar missions generally carried one AGC in the command module and another in the lunar module. The command-module version was called the Command Module Computer, or CMC; the lunar-module version was the Lunar Module Guidance Computer, or LGC. They were mission-specific versions of the same Apollo computer family, not two unrelated systems.

The AGC was extraordinarily constrained by modern standards: it had 2,048 words of erasable memory and 36,864 words of fixed core-rope memory. The Launch Vehicle Digital Computer guided the Saturn rocket during ascent, so it is a related but different machine. Gemini’s computer and IBM System/360 computers did not perform Apollo spacecraft guidance.