Catalyzes the phosphorylation of mevalonate (MVA) to yield mevalonate-3-phosphate. Functions in an alternative mevalonate pathway, which passes through mevalonate 3-phosphate rather than mevalonate 5-phosphate. Also able to catalyze the formation of isobutene via the conversion of 3-hydroxyisovalerate (3-HIV) to an unstable 3-phosphate intermediate that undergoes a spontaneous decarboxylation. (R)-mevalonate + ATP = (R)-3-phosphomevalonate + ADP + H(+) kcat is 1.9 sec(-1) for mevalonate as substrate. kcat is 0.1 sec(-1) for 3-hydroxyisovalerate (3-HIV) as substrate. kcat is 0.1 sec(-1) for 3-hydroxybutyrate (3-HB) as substrate. Isoprenoid biosynthesis; isopentenyl diphosphate biosynthesis via mevalonate pathway. Homodimer. Belongs to the GHMP kinase family.