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A common multiple
Any multiple of 30 is also a multiple of 15.
No, 300 is not a multiple of 24.
The least common multiple (LCM) is often also called the lowest common multiple or smallest common multiple. Keep in mind that these different terms all refer to the same thing: the smallest positive integer which is a multiple of two or more numbers.The least common multiple of 3 and 24 is 24.
"most common multiple" is not a recognised mathematical term. 48 is a common multiple, but it is not the Least Common Multiple (LCM).