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The common multiples of an set of numbers are the multiples of their lowest common multiple. lcm(7, 8, 9) = 504 → the first 3 common multiples of 7, 8, 9 are 504, 1008, 1512.
504 is the least common multiple of 7, 8 and 9. All numbers that are multiples of 504 are multiples of 7, 8 and 9 as well
lcm(2, 7) = 14 → first 3 common multiples are: 14, 28, 42; lcm(2, 8) = 8 → first 3 common multiples are: 8, 16, 24; lcm(7, 8) = 56 → first 3 common multiples are: 56, 112, 168; lcm(2, 7, 8) = 56 → first 3 common multiples are: 56, 112, 168.
All common multiples of 7, 10 and 8 are divisible by them. The lowest common multiple of them is 280, so all multiples of 280 are divisible by them, namely 280, 560, 840, 1120, ...
There are not just three common multiples, but infinitely many. They are 168 and it multiples, so 1680 and 16800.