Let’s take the LCM of 8, 10 and 12

LCM = 2 × 2 × 2 × 3 × 5 = 120

Now to get greatest 3-digit number we have to calculate the multiples of 120

120 × 1 = 120

120 × 2 = 240

120 × 3 = 360

120 × 4 = 480

120 × 5 = 600

120 × 6 = 720

120 × 7 = 840

120 × 8 = 960

120 × 9 = 1080

120 × 10 = 1200

Hence the greatest 3-digit number exactly divisible by 8, 10 and 12 is 960.