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Then the number of ordered pairs $(a,b,c)$ is

My Trail Solution:: First we will factorise in prime factor form.

$\bf{L.C.M}$ of $(a,b)$ is $ = 432 = 2^4 \times 3^3$

Similarly $\bf{L.C.M}$ of $(b,c)$ is $ = 72 = 2^3 \times 3^2$

Similarly $\bf{L.C.M}$ of $(c,a)$ is $ = 432 = 2^4 \times 3^3$

Now Let we assume that $a = 2^l\cdot 3^m$

and Similarly $b = 2^p\cdot 3^q$

and Similarly $c = 2^x\cdot 3^y$,

Now How can i solve after that

Help Required.

Thanks.