3360
Never.
33 is the first composite number that is greater than 30 but is not a multiple of 2
No, for any number n greater than zero, the LCM of n and n is n.
It depends on what the numbers are. For example, if the prime numbers you were talking about were 3 and 7, the least common multiple would be 21. If your numbers were 2 and 3, it would be 6.
400
The first common multiple of 3984 is 3984, itself and that is greater than 300.
The greatest common multiple of any set of integers is infinite.
Never.
1, 2, and 53, have their first common multiple of 106.
The lowest common multiple of 7 and 9 is greater than 40.
This is the lowest common multiple which is the smallest number greater than 0 which is a multiple of all the numbers. for example the lowest common multiple (lcm) of 4 and 6 is 12 as 12 is the first (smallest) number greater than 0 that is a multiple of both 4 and 6.
189, for one.
There is no greatest common multiple. Ever! If x were the greatest common multiple, then what about 2x? Since x is a multiple of 16 and 24 then so also is 2x, so that 2x is a COMMON multiple. And it would certainly be greater that x. So 2x is a common multiple that is greater than the greatest common multiple. What?!
Any multiple of 45 greater than 180, starting with 225.
There can be no greatest common multiple. For, if x were the greatest common multiple, then 2x would be (a) a common multiple and (b) greater than x. So x could not have been the greatest common multiple.
There can never be a greatest common multiple of one number for two reasons:"Common" refers to a multiple that is common to two or more numbers. You cannot have a multiple that is common, but only to one number.If X is the greatest common multiple of a set of numbers, then any multiple of X will also be a common multiple of each member of the set and it will be greater than X. And then, any multiple of this number will be a multiple of each member of the set and will be greater still. And then ...
There can never be a greatest common multiple. If a number, X, is claimed as the greatest common multiple, the 2X is a common multiple, and it is greater than X which contradicts X being the greatest.