Note quite the "Eureka!" experiment

A container of water is sitting on a scale. Originally, the scale reads $M_1 = 45 \, \text{kg}$ . A block of wood is suspended from a second scale; originally the scale read $M_2 = 12 \, \text{kg}$ . The density of wood is $0.60 \, \text{g/cm}^3$ ; the density of the water is $1.00 \, \text {g/cm}^3$ . The block of wood is lowered into the water until half of the block is beneath the surface. Let the reading of $M_1$ be $a \, \text{kg}$ . Let the reading of $M_2$ be $b \, \text{kg}$ , where $a, b$ are integers. Compute $ab$ .

Note : A version of this problem appeared on the 2012 F = ma exam.