# Does $\frac{\mbox{lcm}(1,2,\dots,n+1)}{\mbox{lcm}(1,2,\dots,n)}\to\infty$?

I feel that the answer to the title quesiton is "yes". However, I tried using different bounds on such least common multiples to prove this with no luck. Any input on this is highly appreciated.

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Have you tried $n+1=2p$, where $p$ is a prime? –  damiano Aug 6 '10 at 16:00
Well, it's equal to 1 infinitely often, so... –  Qiaochu Yuan Aug 6 '10 at 16:00
Very helpful hints. Thanks a lot. –  Abdulaziz Aug 6 '10 at 17:19

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