Final answer:
To find the numbers, we set up a system of equations using the given information. By factoring the numbers and finding the LCM, we can determine the values of the numbers. In this case, the numbers are 42 and 47.
Step-by-step explanation:
To find the numbers, we need to set up a system of equations based on the given information. Let's say one of the numbers is x. The other number is 5 less than x, so it would be x - 5.
The least common multiple of x and x - 5 is 84. We can write this as an equation: LCM(x, x - 5) = 84.
To solve this equation, we can factor x and x - 5 into their prime factors and find the LCM. If we factorize x, we get x = 2^a * 3^b * 7^c, and if we factorize x - 5, we get x - 5 = 2^d * 3^e * 7^f.
According to the properties of LCM, the exponents of the prime factors in the LCM should be the maximum of the corresponding exponents in x and x - 5. So, a, b, and c should be the maximum of d, e, and f.
In this case, the maximum of a and d is 2, the maximum of b and e is 1, and the maximum of c and f is 1. Therefore, the LCM would be 2^2 * 3^1 * 7^1 = 84.
This means that the numbers are x = 2^2 * 3^1 * 7^1 = 84 and x - 5 = 79.
So, the answer is (d) 42, 47.