The number of ordered pairs of positive integers (a,b) that can be formed whose lcm is 3^2 * 7^3 * 11 ^4 is
Ordered pair means (a,b) not equal to (b,a) . So i will multiply by 2 for each unique combo.
Power of 3 --> 1,2 ,0
Power of 7 --> 1,2 ,3,0
Power of 11--> 1,2 ,3,4,0
Using bars concept , arranging the bars 1|2 this means that the first number got the factor 3^1 and the 2nd number got the factor 3^2 ...so on
1 2 | --> 3 ways
1,2,3 , | --> 4ways
1,2,3,4, | = 5ways
But in this approach I am missing This type of pair (a,b)-->( 3^0 *7^0 11^4) , (3^2 * 7^3 * 11^3)
Ordered pair means (a,b) not equal to (b,a) . So i will multiply by 2 for each unique combo.
Power of 3 --> 1,2 ,0
Power of 7 --> 1,2 ,3,0
Power of 11--> 1,2 ,3,4,0
Using bars concept , arranging the bars 1|2 this means that the first number got the factor 3^1 and the 2nd number got the factor 3^2 ...so on
1 2 | --> 3 ways
1,2,3 , | --> 4ways
1,2,3,4, | = 5ways
But in this approach I am missing This type of pair (a,b)-->( 3^0 *7^0 11^4) , (3^2 * 7^3 * 11^3)