Smallest 3-digit number = LCM of 6, 8 and 12

LCM = 2 × 2 × 2 × 3 = 24

LCM of these 3 numbers is 24 so to find out 3-digit number we have to calculate the multiples of 24,

24 × 1 = 24

24 × 2 = 48

24 × 3 = 72

24 × 4 = 96

24 × 5 = 120

24 × 6 = 144

It can be seen that, 120 is the smallest 3-digit multiple of 24 so, the smallest 3-digit number which is exactly divisible by 6, 8 and 12 is 120.