< b="" />Explanation:< />

< b="" />Understanding HCF and LCM< />

HCF (Highest Common Factor) is the greatest number that divides two given numbers completely. On the other hand, LCM (Lowest Common Multiple) is the smallest number that is divisible by both the given numbers.

< b="" />Relationship between HCF and LCM< />

The relationship between HCF and LCM of two numbers can be expressed by the formula:
HCF x LCM = Product of the two numbers

< b="" />Given Information< />

In this case, the given information is that the HCF of two numbers is 8. This means that 8 is the greatest number that divides both the numbers completely.

< b="" />Analysis of the options< />

1) 24
- 24 = 8 x 3
- Since 8 is a factor of the HCF, the LCM can be a multiple of 8. Therefore, 24 can be the LCM.

2) 48
- 48 = 8 x 6
- Similar to the previous case, 48 can also be the LCM as it is a multiple of 8.

3) 56
- 56 = 8 x 7
- Again, 56 can be the LCM as it is a multiple of 8.

4) 60
- 60 = 8 x 7.5
- In this case, 60 is not a multiple of 8. Since the HCF is 8, the LCM must be a multiple of 8. Therefore, 60 can never be the LCM of the two numbers.

< b="" />Conclusion< />

Based on the analysis above, the number that can never be the LCM of the two numbers with an HCF of 8 is 60.