To find the Least Common Multiple (LCM) of 4.9 and 0.008, we begin by converting these decimal numbers into fractions for easier calculation.

1. Convert the numbers to fractions:
   • 4.9 can be written as the fraction \frac{49}{10}.
   • 0.008 can be expressed as the fraction \frac{8}{1000}, which simplifies to \frac{1}{125}.
2. The LCM of two fractions \frac{a}{b} and \frac{c}{d} is given by the formula:

   \text{LCM}\left(\frac{a}{b}, \frac{c}{d}\right) = \frac{\text{LCM}(a, c)}{\text{GCD}(b, d)}

3. In our case:
   • Calculate LCM of the numerators: LCM(49, 1) = 49, because 49 is the largest number.
   • Calculate GCD of the denominators: GCD(10, 125).
4. To find the GCD of 10 and 125, observe their prime factors:
   • Prime factors of 10 = 2 × 5
   • Prime factors of 125 = 5 × 5 × 5
   • The common factor is 5.

   Thus, GCD(10, 125) = 5.

5. Substitute the values into the LCM formula for fractions:

   \text{LCM}\left(\frac{49}{10}, \frac{1}{125}\right) = \frac{49}{5}

6. Convert the fraction back to a decimal to find the LCM:

   \frac{49}{5} = 9.8

Therefore, the LCM of 4.9 and 0.008 is 9.8, which matches option 9.8.

By working through these steps, we confirmed the correct option is 9.8, while the other options do not match the computed LCM.