There is an infinite number of common multiples for 3 and 5. A common multiple of any two or more numbers is any number into which each of two or more numbers can be divided evenly (zero remainder). However, the least or lowest common multiple (LCM) of 3 and 5 is 15.
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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]).
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...
Since all 3 are prime numbers LCM = 3 * 5 * 7 = 105 All multiples of 105 are multiples of 3, 5 and 7
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.