Explanation:

- We know the HCF (highest common factor) of 108, 72, and 5a is a.

- 108 = 2³ × 3³

- 72 = 2³ × 3²

- HCF(108, 72) = 2³ × 3² = 72

- Now, HCF(72, 5a) = a (implies 5a shares no factor with 72 except a)

- As 72 and 5 have no common factor, the only way HCF(72, 5a) = a is if a divides 72.

- For the least LCM, a should be as small as possible, so a = 1 or a factor of 72.

- For LCM(108, 72, a):

- If a = 1: LCM = LCM(108, 72, 1) = LCM(108, 72) = 216

- Option 4: 216 is possible.

- Option 1: 432 is more than required.

- Option 2: 324 isn't a multiple of both 108 and 72.

- Option 3: 108 isn't divisible by both 108 and 72.

Option 4: 216 is the correct answer.