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Sum Inverse LCMs (Posted on 2008-10-03) Difficulty: 3 of 5
Each of P, Q, R, S and T are positive integers with P < Q < R < S < T. Determine the maximum value of the following expression.

[P, Q] -1 + [Q, R] -1 + [R, S] -1 + [S, T] -1

Note: [x, y] represents the LCM of x and y.

No Solution Yet Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

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Solution Solution | Comment 4 of 7 |
The maximum value is where each positive integer, P, Q, R, S, and T, is a power of 2.

[20, 21]-1 = 1/2
[21, 22]-1 = 1/4
[22, 23]-1 = 1/8
[23, 24]-1 = 1/16

1/2 + 1/4 + 1/8 + 1/16 = 15/16


  Posted by Dej Mar on 2008-10-03 21:22:54
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