609, 618, 627, 636, 645, 654, 663, 672, 681, and 690 all meet these conditions.
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The rules of divisibility tell you that 63 is divisible by 1 (because all integers are), 3 (because its digits total a multiple of 3) and 9 (because its digits total a multiple of 9) Dividing those numbers into 63 gives you the other three (63, 21 and 7) (1, 3, 7, 9, 21, 63)
780 is divisible by 2 because it's even. 780 is divisible by 3 because its digits total a multiple of 3. 780 is divisible by 5 because it ends in a 0. 780 is divisible by 10 because it ends in a 0.
Add the digits. If the total is divisible by three, the original number is divisible by three. It's not and it's not.
The total number of integers that are multiples of both 42 and 56 is infinite. Here are the first few: 168, 336, 504, 672, 840 . . .
Total product is the sum of all marginal products.