Be the product of the two numbers?

A) 25
B) 48
C) 72
D) 90

We can approach this problem by using the fact that the product of two numbers is equal to the product of their LCM and GCD (Greatest Common Divisor).

Let's assume the two numbers are x and y. We know that LCM(x,y) = 84. We need to find the product of x and y, which is xy.

We can write the following equation:

xy = LCM(x,y) * GCD(x,y)

Since the LCM is 84, we can rewrite the equation as:

xy = 84 * GCD(x,y)

From this equation, we can see that the product of x and y must be a multiple of 84. Therefore, we can eliminate options A (25 is not a multiple of 84) and D (90 is not a multiple of 84).

Now, we need to find the GCD of two numbers whose LCM is 84. We can use the fact that:

LCM(x,y) * GCD(x,y) = xy

Since LCM(x,y) = 84, we can rewrite the equation as:

84 * GCD(x,y) = xy

We need to find two numbers whose product is a multiple of 84 and whose GCD is a factor of 84. We can list all the factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.

We can then try to find two numbers whose product is a multiple of 84 and whose GCD is one of these factors.

Option B (48) can be written as 2 * 24. We can see that 2 is a factor of 84, but 24 is not. Therefore, option B is not possible.

Option C (72) can be written as 6 * 12. We can see that both 6 and 12 are factors of 84. Therefore, option C is possible.

Therefore, the answer is C) 72.

8 is the answer