lcm(1, 79) + lcm(2, 79) + lcm(3, 79) + ... + lcm(79, 79) = ?
Note: Here lcm means the least common multiple
(In reply to
Puzzle Answer by K Sengupta)
We know that:
gcd(n,79)=1, where n=1,2,....,78
and, gcd(79,79)=79
=> lcm(n,79)= 79*n, where n=1,2,.....,78
and, lcm (79,79) = 79
79 78
Then, SUM lcm (i,79) = SUM lcm (I,79) + lcm(79,79)
i= 1 i=1
78
= 79{ SUM } +79
i= 1
= 79{(78*79)/2 +1 }
=79*3082
= 243,778
Edited on May 17, 2022, 10:47 pm
Explanation to Puzzle Answer
