LCM is between 100 and 200 and their greatest common factor is 64

The possible numbers are,

64 and 128 or 64 and 192

Step-by-step explanation:

Given,

The greatest common factor of two numbers is 64,

Let first number = 64x and second number = 64y

Where,

GCF (x, y) = 1,

Now, LCM (64x, 64y) = 64xy,

According to the question,

100 < 64xy < 200

⇒ 1.5625 < xy < 3.125

⇒ xy = 2 or 3 (∵ xy must be a whole number)

If xy = 2,

⇒ x = 1, y = 2 or x = 2, y = 1

Thus, the numbers are 64 and 128.

If xy = 3,

⇒ x = 1, y = 3 or x = 3, y = 1

Thus, the numbers are 64 and 192.