Question

If the greatest common factor (GCF) of (8, b) is 12 and the least common multiple (LCM) of (8, b) is 48, what is the value of b?

a) 3
b) 6
c) 9
d) 12

Answer 1

The value of b is 6.

Step-by-step explanation:

To find the value of b, we need to determine the prime factorization of both 8 and 12. The prime factorization of 8 is 2 x 2 x 2 and the prime factorization of 12 is 2 x 2 x 3. Since the GCF is 12, which is a factor of 8, it means that b must have at least one factor of 2, but not 3. Since 48 is the LCM, we know that 8 is a factor of 48, so b must also have a factor of 2, as well as the additional factor of 3. Therefore, b must be a multiple of 6. The only option that is a multiple of 6 is (b) 6.