12
12 is the smallest multiple of 3 and 4.
I assume you mean LCM, least common multiple. The least common multiple of 3 and 4 is 12. 12 is a multiple of 3. 12 is a multiple of 4. No smaller number is a multiple of both 3 and 4.
Any multiple of 12
4 is an even number and so all multiples of 4 must be even. A number ending in 3 is not even and so cannot be a multiple of 4.
The LCM of 3 and 4 is 12.
To test if a number is a multiple of 3, add the digits together and if the result is a multiple of 3, the original number is also a multiple of 3: 11154: 1 + 1 + 1 + 5 + 4 = 12 = 3 x 4, a multiple of 3, thus 11154 is a multiple of 3. (11154 = 3 x 3718)
A number that ends in 3 can't be a multiple of 4 because the 4 times table goes in a pattern, (e.g 4, 8, 12, 16, 20, 24.) If the number ends in either 0 2 4 6 8 then it couldbe a possible multiple of 4. It always ends in an even number. 3 is not an even number so it is not going to be the last number of a multiple of 4.
A common multiple of 3 and 4 is a number which is a multiple of 3 and of 4. The first 3 common multiples of 3 and 4 are 12, 24, 36
12
The greatest 4 digit integer divisible by 3 (and therefore a multiple of 3) is 9999.
There is no such number. If X were a common multiple of 4 and 3 then a number of the form k*X (where k is any integer) would also be a multiple. There is no limit to how large k can be and so no greatest multiple.
The number is a multiple of 3 and 4 at the same time