There are infinitely many common multiples of 3, 5 and 7, each one 105 larger than the previous one.
Or to put it another way: the common multiples of 3, 5 and 7 are the multiples of their lowest common multiple which is 105. ie their common multiples are all the multiples of 105, of which there is no end - there is an infinite number of multiples of 105 (or any other number [except zero]).
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60 and its multiples
Since the lowest common multiple of 3 and 5 is 15, the common multiples of 3 and 5 are the multiples of 15: 30, 45, 60, 75, 90, etc...
lcm(2, 3, 5) = 30 → 2 digit common multiples are 30, 60, 90.
The LCM of 3 and 5 is 15. The multiples of 3 are , 6, 9, 12, 15, and so on. The multiples of 5 are 5, 10, 15, and so on. The LCM is 15.
The first common multiples of 5, 3, and 8 are found by listing out the multiples of each number and finding the least common multiple. The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, and so on. The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, and so on. The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, and so on. The first common multiples of 5, 3, and 8 are 24 and 48.