Multiplication is the same as repeated addition.
For example
12 * 3 = 12 + 12 + 12
12 * 4 = 12 + 12 + 12 + 12
and so on.
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Addition, subtraction and multiplication.
You can have counting number in multiplication and addition. All integers are in multiplication, addition and subtraction. All rational numbers are in all four. Real numbers, complex numbers and other larger sets are consistent with the four operations.
If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.
The answer depends on which binary operation you mean when you say "combining". Addition, subtraction, multiplication, division, exponentiation, etc.
It means nothing, really. The distributive property is a property of multiplication over addition or subtraction. It has little, if anything, to do with integers.