In mathematics, the greatest common divisor (gcd) of two or 
more integers, which are not all zero, is the largest 
positive integer that divides each of the integers. 
For example, the gcd of 8 and 12 is 4

> gcd2 :: Int -> Int -> Int
> gcd2 a b = 
>    if  | b /= 0    -> gcd b (mod a b)
>        | otherwise -> a

The greatest common divisor can be used to find the least 
common multiple of two numbers when the greatest common 
divisor is known, using the relation

> lcm :: Int -> Int -> Int
> lcm a b = (a*b) `div` gcd2 a b

\begin{code}
gcd2 :: Int -> Int -> Int
\end{code}

#!/usr/bin/ghci

(*) Find the last element of a list.
(Note that the Lisp transcription of this problem is incorrect.)
Example in Haskell:

myLast [1,2,3,4]
4
myLast ['x','y','z']
'z'

Assume that input type is list of 'a' type and output is 'a' type.

> myLast :: [a] -> a

Empty input will throws an error.

> myLast []     = error "Unable to get last from []"

Last element will be first when tail is empty

> myLast (h:[]) = h

Otherwise, if tail of tail is empty then get head of tile, Otherwise proceed 'myLast' for tile

> myLast (h:t)  = if (null (tail t)) then (head t) else (myLast t)

#!/bin/bash

ctangle gcd-lcm.w gcd-lcm.c
cweave  gcd-lcm.w gcd-lcm.tex

@*LCD-LCM

In mathematics, the greatest common divisor (gcd) of two or 
more integers, which are not all zero, is the largest 
positive integer that divides each of the integers. 
For example, the gcd of 8 and 12 is 4

@c*
#include <stdio.h>
int gcd(int a, int b) {
  if (b != 0)
    return gcd(b, a % b);
  else
    return a;
}

@
The greatest common divisor can be used to find the least 
common multiple of two numbers when the greatest common 
divisor is known, using the relation

@c*
int lcm(int a,int b) {
  return (a * b) % gcd(a,b);
}
@* Index.