correct answer is: a) 217\large\frac{1}{2} dm

Explanation

Two wheels circumferences are 6\large\frac{3}{14} and 8\large\frac{1}{18} dm.
Or, \large\frac{87}{14} and \large\frac{145}{18} _{[covert mixed to improper]}
Two find the least distance travelled by the car we need to find the LCM of wheels circumferences.
We know,
The formula we use to get the LCM of two or more fractions is:
\large\frac{The\ LCM\ of\ Numerator}{The\ HCF\ of\ Denominator}

\rightarrow LCM of Numerators 87 and 145 =3\times5\times29=435
\rightarrow HCF of Denominators 14 and 18 is =2
So that, the LCM of 6\large\frac{3}{14} and 8\large\frac{1}{18} is =\large\frac{435}{2} or 217\large\frac{1}{2}
Hence, the least distance travelled by the car is 217\large\frac{1}{2} dm.
Ans: 217\large\frac{1}{2} dm.

Another method to articulate this particular math query is available:

1. Finding the minimum car travel distance as its wheels rotate integer times, with wheel circumferences of 6 3/14 dm and 8 1/18 dm.
2. What is the shortest distance covered by a car with wheels rotating whole number times, given their circumferences of 6 3/14 dm and 8 1/18 dm?
3. Finding the least distance covered by a car as its wheels rotate whole numbers of times, with circumferences of 6 3/14 dm and 8 1/18 dm.