perplexus.info :: Numbers : LCM equation

LCM equation (Posted on 2013-11-19)

The least common multiple (LCM) of 2 numbers is the smallest number that they both divide evenly into.
e.g.:
LCM(8,10)=40
LCM(17,11)=187

For any integer n, show that LCM(9n + 8, 6n + 5) = 54n^2 + 93n + 40.

No Solution Yet Submitted by Ady TZIDON

Rating: 4.3333 (3 votes)

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Proof

| Comment 5 of 6 |

GCD(9n+8, 6n+5)=GCD(6n+5, 3n+3)=GCD(3n+3, 3n+2)=GCD(3n+2, 1)=1

Therefore, LCM(9n+8, 6n+5)=(9n+8)(6n+5)=54n^2+93n+40.

Posted by Math Man on 2013-11-26 22:57:04

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