what is the lcm of ((3^501)-1),((3^501)+1)......??

• 3^501-1 and 3^501+1 are 2 consecutive even nos,so their HCF will be 2.
  HCF x LCM=((3^501)-1)x((3^501)+1)
  2 x LCM= (3^501)^2 - 1^2
  LCM= ((3^1002)-1)/2
• 10 years agoHelpfull: Yes(22) No(0)
• LCM(a^m -1, a^m +1) is
  a^2m -1 , if a is even
  (a^2m -1)/2 , if a is odd
  Here a^2m -1 is nothing but product of 2 numbers => (a^m -1)* (a^m +1) = a^2m -1
  Check for small numbers
  LCM(2^3 -1 , 2^3 +1) => 2^2(3) -1 = 63 [Since a is even]
  LCM(5^2 -1 , 5^2 +1) => [5^2(2) -1]/2 = 312 [since a is odd]
  
  Hence LCM(3^501 -1, 3^501 +1) => [3^2(501) -1]/2 [Since a is odd]...
  
  Ans : [3^1002 -1]/2
• 10 years agoHelpfull: Yes(12) No(0)
• ans will be ((3^1002)-1)/2
• 10 years agoHelpfull: Yes(2) No(1)