Final answer:
The two numbers whose least common multiple is 84 and have a difference of 5 are 12 and 7. By analyzing the prime factorization of 84 and given conditions, we determine that these two numbers satisfy the question's requirements.
Step-by-step explanation:
To find the two numbers whose least common multiple (LCM) is 84 and have a difference of 5, we can start by listing the factors of 84 and look for a pair of numbers with a difference of 5.
The factors of 84 that meet this criteria are 14 and 7. However, to have a difference of 5, we need to find a different pair of factors.
Now, consider the given condition that one number is 5 less than the other. If 'x' is one number, the other number is 'x - 5'.
Their LCM, which we know is 84, can be thought of as a product of prime factors: 84 = 22 × 3 × 7. With these factors in mind, we look for a pair of numbers such that their product is a multiple of 84 and they have a difference of 5.
Upon inspection, the numbers 12 and 7 satisfy both conditions. We have 12 × 7 = 84, and 12 is 5 more than 7. Therefore, the two numbers in question are 12 and 7.