The highest common multiple is an infinite amount and not very practical for problem solving.
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There is no highest common multiple of 14 and 16. Whatever common multiple you come up with as the highest I can always add the lowest common multiple of 14 and 16 (122) to it and get a higher common multiple of 14 and 16.
The Least Common Multiple (LCM) for 12 14 is 84.
The LCM of 13, 14, and 15 is 2730.2730
The LCM of 8, 12 and 3 is 24
84