1: L.C.M of (a,b) is 432,

L.C.M of (b,c) is 72,

L.C.M of (a,b) is 432.

Find the number of ordered pairs (a,b,c).

2: Find the number of triplets satisfying abc=60.

hi mehul

the l.c.m (a,b) = 2^4*3^3

l.c.m (b,c) = 2^3*3^2

l.c.m (c,a) = 2^4*3^3

the max value of b,c = 2^3*3^2

(2^3*3^2,2^3*3^2)

(2^3*3^2,2^3*3^1)

(2^3*3^2,2^3*3^0)  similarly for 2^b

we get 7 and now interchanging b,c

we have 6 more one case when both are same

so 13 triplets