Q13/115) If L.C.M of (a,b) is 432, and L.C.M of (b,c) is 72, and L.C.M of (c,a) is 432. Then the number of ordered pairs (a,b,c) is

LCM of  (a,b) is =432=2^4×3^3

LCM of  (b,c) is =72=2^3×3^2

 LCM of of (c,a) is =432=2^4×3^3

First find power of 2

Highest from LCM of (b,c) = 3 so  b cannot have power > 3 and c cannot power > 3

So power of 2 in a = 4

Now in b and c can be (3,0), (3,1), (3,2), (3.3), (0,3),(1,3),(2,3) as these combinations given power 3

Similarly you can find the power of 3

In a = 3 an in bc = (2,0),(2,1)(2,2),(1,2),(0,2)

So a = 432 and for bc there are 35 sets

for example one is (2^3*3^2,1)