is that statement always true, give evidence
Is A and B are whole numbers, then A x B is a common multiple of A and B
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: