Ruby, 101 86 91 90 bytes

A Ruby port of my Actually answer. Golfing suggestions welcome.

Edit: -4 bytes from removing a but +9 bytes from fixing a bug where 1 returned nil. -1 byte thanks to Cyoce.

require'prime'
->n{((n%8<1?n/2:n).prime_division<<[2,1]).map{|x,y|x**~-y*~-x}.reduce :lcm}

Ungolfing

require 'prime'
def carmichael(n)
  if n%8 < 1
    n /= 2
  end
  a = []
  n.prime_division.do each |x,y|
    a << x**(y-1)*(x-1)
  end
  return a.reduce :lcm
end

Ruby, 101 86 91 90 bytes

A Ruby port of my Actually answer. Golfing suggestions welcome.

Edit: -4 bytes from removing a but +9 bytes from fixing a bug where 1 returned nil. -1 byte thanks to Cyoce.

require'prime'
->n{((n%8<1?n/2:n).prime_division<<[2,1]).map{|x,y|x**~-y*~-x}.reduce :lcm}

Ungolfing

require 'prime'
def carmichael(n)
  if n%8 < 1
    n /= 2
  end
  a = []
  n.prime_division.do each |x,y|
    a << x**(y-1)*(x-1)
  end
  return a.reduce :lcm
end

Ruby, 101 86 91 bytes

A Ruby port of my Actually answer. Golfing suggestions welcome.

Edit: -4 bytes from removing a but +9 bytes from fixing a bug where 1 returned nil

require'prime'
->n{((n%8<1?n/2:n).prime_division<<[2,1]).map{|x,y|x**~-y*~-x}.reduce(:lcm)}

Ungolfing

require 'prime'
def carmichael(n)
  if n%8 < 1
    n /= 2
  end
  a = []
  n.prime_division.do each |x,y|
    a << x**(y-1)*(x-1)
  end
  return a.reduce(:lcm)
end

Ruby, 101 86 91 90 bytes

A Ruby port of my Actually answer. Golfing suggestions welcome.

Edit: -4 bytes from removing a but +9 bytes from fixing a bug where 1 returned nil. -1 byte thanks to Cyoce.

require'prime'
->n{((n%8<1?n/2:n).prime_division<<[2,1]).map{|x,y|x**~-y*~-x}.reduce :lcm}

Ungolfing

require 'prime'
def carmichael(n)
  if n%8 < 1
    n /= 2
  end
  a = []
  n.prime_division.do each |x,y|
    a << x**(y-1)*(x-1)
  end
  return a.reduce :lcm
end

Ruby, 101 86 bytes

A Ruby port of my Actually answer. Golfing suggestions welcome.

require'prime'
->n{n=n%8<1?n/2:n
a=n.prime_division.map{|x,y|x**~-y*~-x}.reduce(:lcm)}

Ungolfing

require 'prime'
def carmichael(n)
  if n%8 < 1
    n /= 2
  end
  a = []
  n.prime_division.do each |x,y|
    a << x**(y-1)*(x-1)
  end
  return a.reduce(:lcm)
end

Ruby, 101 86 91 bytes

A Ruby port of my Actually answer. Golfing suggestions welcome.

Edit: -4 bytes from removing a but +9 bytes from fixing a bug where 1 returned nil

require'prime'
->n{((n%8<1?n/2:n).prime_division<<[2,1]).map{|x,y|x**~-y*~-x}.reduce(:lcm)}

Ungolfing

require 'prime'
def carmichael(n)
  if n%8 < 1
    n /= 2
  end
  a = []
  n.prime_division.do each |x,y|
    a << x**(y-1)*(x-1)
  end
  return a.reduce(:lcm)
end