The largest three-digit number divisible by both 3 and 4 is 996.
Here's how we arrive at that answer:
Since a number divisible by both 3 and 4 must also be divisible by their least common multiple (LCM), we first find the LCM of 3 and 4. The LCM of 3 and 4 is 12.
Therefore, we are looking for the largest three-digit number divisible by 12.
To find this number, we can start by dividing the largest three-digit number, 999, by 12:
999 / 12 = 83.25
Since we need a whole number, we take the integer part of the result (83) and multiply it by 12:
83 * 12 = 996
Therefore, 996 is the largest three-digit number that is divisible by both 3 and 4 (and thus divisible by 12).
