The LCM of two numbers is 24. The GCF is 2. The numbers differ by 2. What are the numbers?

what does six and eight have in common?

kjefieug

To find the two numbers, we need to use the relationship between the least common multiple (LCM), greatest common factor (GCF), and the difference between the numbers.

Step 1: Let's first express the given information mathematically.
Let's represent the two numbers as "x" and "y" such that x > y. Given:
LCM(x, y) = 24
GCF(x, y) = 2
x - y = 2

Step 2: Understanding the relationship between LCM and GCF.
The relationship between LCM and GCF is given by the formula:
LCM(x, y) * GCF(x, y) = x * y

Step 3: Substitute the given values into the formula.
Using the values given in the problem, we can substitute them into the formula:
24 * 2 = x * y
48 = x * y

Step 4: Find the factors of 48.
We need to find the factors of 48 that differ by 2. Let's list the factors:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Among the factors, the pairs that have a difference of 2 are:
4 and 6
6 and 8

Step 5: Determine the values of x and y.
Since x > y, we can conclude that x = 8 and y = 6.

Therefore, the two numbers are 8 and 6.