If the product of two numbers is 24 and the LCM is 12, what are the two numbers?

X, y, and z are different prime numbers. What is the LCM of x, y, and z?

LCM of any set of primes is their product, since they have no factors in common

6*4=24
LCM(6,4) = 12

To find the two numbers, we can use the concept of the least common multiple (LCM) and the product of the numbers.

Let's assume the two numbers are x and y.

We are given that the product of the two numbers is 24, so we can write the equation:
x * y = 24

We are also given that the LCM of the two numbers is 12. The LCM is the smallest multiple that both numbers have in common. So, we can set up the second equation using the LCM:
LCM(x, y) = 12

To find the two numbers, we can proceed by listing the factors (the numbers that divide evenly into a given number) of 24 and the prime factorization.

Prime factorization of 24 = 2 * 2 * 2 * 3

Now, let's list the factors of 24:
1, 2, 3, 4, 6, 8, 12, 24

We'll try to find two numbers whose product is 24 and whose LCM is 12.

Considering the prime factorization, we can select factors in pairs that multiply to 24 and have a common multiple of 12:
(2 * 2) and (2 * 3) or (4) and (6)

So, the two numbers are 4 and 6, since multiplying them gives 24 and their LCM is 12.

Therefore, the two numbers are 4 and 6.