LCM of 6, 9 and 12 = 36 and largest 3-digit number = 999 HCF of 36 and 999
∴ Largest three-digit number completely divisible by 6, 9 and 12 = 999 – 27 = 972 Since 3 is left as remainder in each case, ∴ Required largest number of 3-digit = 972 + 3 = 975.