-- See: http://en.wikipedia.org/wiki/Least_common_multiple

function lcm (a, b)
  a = bc.number (a)
  b = bc.number (b)
  return (a * b) / gcd (a, b)
end -- lcm

print (lcm (21, 6))  --> 42
print (lcm (4, 6))   --> 12

-- See: http://en.wikipedia.org/wiki/Greatest_common_divisor
-- and  http://en.wikipedia.org/wiki/Euclidean_algorithm

function gcd (a, b)
local old_digits = bc.digits (0)  -- we are using integers
local temp

  a = bc.number (a)
  b = bc.number (b)

  while not bc.iszero (b) do  
     temp = b
     b = bc.mod (a, b)
     a = temp
  end -- while
  
  bc.digits (old_digits)  -- put old decimal places back
  return a
end -- gcd

print (gcd (8, 12))   --> 4
print (gcd (42, 56))  --> 14
print (gcd (206, 40)) --> 2
print (gcd (12070, 41820)) --> 170
print (gcd (10362, 12397)) --> 11

0.5
-1.75
1.0625
-0.87109375
-1.241195679
-0.459433287
-1.788921055
1.20023854
-0.559427448
-1.687040931
0.846107103
-1.284102771
-0.351080073
-1.876742782
1.52216347
0.316981629
-1.899522647
1.608186286
0.58626313
-1.656295543

0.50001
-1.74999
1.062465
-0.871168124
-1.241066099
-0.459754937
-1.788625398
1.199180813
-0.561965379
-1.684194913
0.836512505
-1.300246828
-0.309358186
-1.904297513
1.626349018
0.645011127
-1.583960646
0.508931328
-1.740988903
1.031042361

bc.digits (100)

function ln (x)
  local x = bc.number (x)  -- argument converted to bignum

  -- if x <= 0.5 or >= 2 take the square root and double the result
  if bc.compare (x, 0.5) ~= 1 or bc.compare (x, 2) == 1 then
    return ln (bc.sqrt (x)) * 2
  end -- if x <= 0.5 or >= 2

  local a = bc.number ((x - 1) / (x + 1))
  local e = bc.number (0)
  local t = bc.number (a)

  for i = 1, 200, 2 do
   local E = e
   
   e = e + (t / i)
   t = t * a * a
    
   -- break if no change
    if e == E then
      break
    end -- if no change

  end -- for 

  return e * 2
end -- function ln

print (ln (100))

Output

4.6051701859880913680359829093687284152022029772575459520666558019351452193547049604719944101791965216

bc.digits (100)

function exp (x)

  local x = bc.number (x)  -- argument converted to bignum

  -- if x > 1 halve it and square the result
  if bc.compare (x, 1) == 1 then
    return exp (x / 2) ^ 2
  end -- if x > 1

  local e = bc.number (1)  -- result

  local n = bc.number (1)  -- denominator: i!
  local t = bc.number (1)  -- numerator:   x^i

  for i = 1, 200 do
    local E = e
    n = n * i  -- n is i!  (factorial of i)
    t = t * x  -- t is x^i (x to the power i)
    e = e + (t / n)  -- new value

    -- break if no change
    if e == E then
      break
    end -- if no change
  end -- for

  return e

end -- function exp

print (exp (5))

Output

148.4131591025766034211155800405522796234876675938789890467528451109120648209585760796884094598990189279

function tangent (x, precision)
  return (sine (x, precision) / cosine (x, precision))
end -- tangent

print (tangent (1, 35))

Output

1.5574077246549022305069748074583601730872507723815200383839466056988613971517272895550999652022429935

pi = bc.number (
"3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706")

function cosine (x, precision)
  return sine (pi / 2 - x, precision)
end -- cosine

print (cosine (1, 35))

Output

0.5403023058681397174009366074429766037323104206179222276700972553811003947744717645179518560871830860

bc.digits (100)

function sine (x, precision)
   local val = bc.number (1)
   x = bc.number (x)
   while precision > 0 do
       val = 1 - val * x * x / (2 * precision) / (2 * precision + 1)
       precision = precision - 1
   end -- while
   val = x * val
   return val
end -- function sine

print (sine (1, 35))

Output

0.8414709848078965066525023216302989996225630607983710656727517099919104043912396689486397435430526959

bc.digits (103)

n = bc.number (1)
e = bc.number (1)

for i = 1, 200 do
  local E = e
  n = n * i   -- n is i! (factorial of i)
  e = e + (1 / n)
  if e == E then
    break
  end -- if no change
end -- for

print (e) 

Output
 2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274229

for i = 1, 1000000 do
  for j = 1, 1000000 do
    for k = 1, 1000000 do
      print("123")
    end
  end
end