First find the least common multiple. To do this, prime factorize them all; we have: 3, 22, 5, and 2 * 3. Each factor is included in the final factorization as often as in each occurs the most. Thus we have 22 * 3 * 5 = 60. Therefore, any multiple of 60 is a multiple of 3, 4, 5, and 6.
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60 and its multiples
5
8/10/12
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...
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]).