How many pairs of positive integers, without regard to order, have a least common multiple of 540?

(In reply to

One for column A, and one .. (spoiler?) by Steve Herman)

....**without regard to order:**

**One should count pairs e.g. 20*27, is one pair - not two.**

**Still I like your approach**, just discount the 540,540 pair ,divide by 2 to get an a<b pair then add the symmetric pair and you get **53.**

- which I believe is the correct answer.

I got 52 and do not have the time to find where is the miss.

*Edited on ***December 22, 2014, 8:38 pm**