The greatest common multiple of any set of integers is infinite.
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"most common multiple" is not a recognised mathematical term. 48 is a common multiple, but it is not the Least Common Multiple (LCM).
The GCF of 48 and 390 is 6.
The GCF is 6.
The Least Common Multiple (LCM) for 6 8 16 is 48.
The GREATEST common multiple is a number approaching infinity. The LEAST common multiple is 540.