Jawab dan Penjelasan dengan langkah-langkah:

“If A and B are whole numbers, then A × B is a common multiple of A and B.”

That statement is always true.

Proof

Whole numbers are a set of numbers including all positive integers and 0.

Let A and B be both whole numbers. To simplify the proof, we can pick two distinct numbers for A and B that are greater than 2.

The multiples of A are:

A×1, A×2, ..., A×B, A×(B+1), ...

The multiples of B are: (in commutative way of multiplication compared to the above one)

1×B, 2×B, ..., A×B, (A+1)×B, ...

From all of the multiples of A and B, we have a multiple that is shown in both lists, which is A × B.

∴  Therefore, A × B is a common multiple of A and B.

Using real examples:

Let A = 3, and B = 4.

The multiples of A are:

3, 6, 9, 12, 15, ...

The multiples of B are:

4, 8, 12, 16, ...

The first common multiple we have found is 12.

12 = 3 × 4 = A × B

12 = 4 × 3 = B × A = A × B

Conclusion:

The statement “If A and B are whole numbers, then A × B is a common multiple of A and B.” is always true.