not sure of this...

1)

analysing data,we can see that a b and c are multiples of 5 and 2 only

also since LCM of a and b has 2 power 3, none of a and b can have term 2^4

since ac and bc LCMs have 2^4 term, c MUST have 2^4 term

so for shuffling powers of 2 between a and b

we have a=3,b=0,1,2,3 or vice versa

hence 2*4 sets=8 possiblities

now for power 5...

we can see that to maintain an LCM of 5^3 for all three cases,

we need to keep atleast 2 terms with power 5^3

other can take powers 0,1 or 2

so for shuffling pors of 5 we have 3*3=9 sets

 

so number of possibilities is

8*9=72