In acute leukemia, bone marrow suppression might happen. Then cancer cell can suppress the nearby cell in the bone marrow, causing a decrease in all blood component (pancytopenia). One of the blood components is thrombocyte which has a function in blood coagulation.
The black and blue marks probably a bruise that made from coagulation problem that caused by low in the blood thrombocyte/platelet count. The suppression should already happen when the bruise shows up.