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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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Puzzle Solution

Comment 6 of 6 |

We observe that for integers 2 and -3,

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

Therefore, in terms of Bezout's Lemma, we must have:

gcd(9n+8, 6n+5) = 1

We know that:

a*b

lcm(a,b) = ---------------

gcd(a,b)

Then, lcm(9n+8, 6n+5)

= (9n+8)(6n+5), since gcd(9n+8,6n+5) = 1

= 54n^2 + 45n+48n+40

= 54n^2 +93n+40

Edited on May 21, 2022, 10:18 am

Posted by K Sengupta on 2022-05-18 23:53:29

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