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$126000=2^4\times 3^2 \times 5^3 \times 7$

Therefor we can assume,

$a=2^{x_1} \times 3^{x_2} \times 5^{x_3} \times 7^{x_4}$

$b=2^{y_1} \times 3^{y_2} \times 5^{y_3} \times 7^{y_4}$

Now by definition of LCM ,

$max(x_1,y_1)=4$

$max(x_2,y_2)=2$

$max(x_3,y_3)=3$

$max(x_4,y_4)=1$

For $max(x_1,y_1)=4$ the choices are $\{(4,0),(4,1),(4,2),(4,3),(4,4),(3,4),(2,4),(1,4),(0,4)\}$

That means there $2 \times 4+1=9$ choices for $max(x_1,y_1)=4$

Similarly , there are $2 \times 2+1=5$ choices for $max(x_2,y_2)=2$

$2 \times 3+1=7$ choices for $max(x_3,y_3)=3$

$2 \times 1+1=3$ choices for $max(x_4,y_4)=1$

So the number of ordered pair is $9\times 5\times 7\times 3=945$

Therefor number of un-ordered pair is $\frac{945-1}{2}+1=\fbox{473}$

LCM of {a , b} = 1,26,000 = 2^4 x 3^2 x 5^3 x 7 If 2^4 / a then b can be 2^0 , 2^1 , 2^2 , 2^3 ,2^4.... and then if 2^4 / b then a can be 2^0 , 2^1 , 2^2 , 2^3 , 2^4.. therefore a and b may have LCM 2^4 in 5 + 5 - 1 = 9 ways Similarly for 3^2, number of ways = 5 Similarly for 5^3, number of ways = 7 Similarly for 7, number of ways = 3 So, number of ordered pairs = 9 x 5 x 7 x 3 = 945 Number of unordered pairs = 945+1/2 = 946/2 = 473