It is infinite
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Highest common multiple of 24 and 18 is 6.
lim_{n \to \infty} 12n = \infty
There is no highest common multiple. Whatever common multiple you come up with as being their highest common multiple, I can always add their lowest common multiple (120) to get a higher common multiple.
There is really no such thing as a "highest common multiple". Once you find the least common multiple of a set of numbers, you can keep adding the LCM to itself over and over again. Each new number you get will be a common multiple of your set of numbers, but each new number will always be larger than the previous. This means that you can keep adding while the number approaches infinity and you will still never find a highest multiple.
LCM is 27, which is the multiple of the highest power of prime factors in the given numbers (33).