Final answer:
The product of the numbers 15 and 3 is indeed equal to the product of their HCF (3) and LCM (15), verifying the relationship. This example in mathematics, suitable for a middle school level, illustrates a key concept in the study of factors and multiples.
Step-by-step explanation:
The relationship that "The product of the numbers equals the product of their HCF (highest common factor) and LCM (least common multiple)" is a fundamental concept in number theory, particularly in mathematics relevant to middle school education. To illustrate this with the pair (15, 3), we need to first determine the HCF and LCM of these two numbers.
The HCF of 15 and 3 is 3 because it is the largest number that divides both 15 and 3 without leaving a remainder. The LCM of 15 and 3 is 15, because it is the smallest number that both 15 and 3 can divide into without leaving a remainder. Now, according to the relationship, the product of the numbers (15 * 3) should be equal to the product of their HCF and LCM (3 * 15).
By performing the calculations, we find that 15 * 3 = 45 and also that 3 * 15 = 45, confirming the relationship is true for this pair of numbers. This demonstrates that the mathematical rule holds, which is very useful when dealing with problems involving multiples and factors.