Find LCM

Script for finding LCM ( least common multiple )

In arithmetic and number theory , the least common multiple (also called the lowest common multiple or smallest common multiple) of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is a multiple of both a and b. It is familiar from grade-school arithmetic as the "lowest common denominator" that must be determined before two fractions can be added.  
                                               - wikipedia ( http://en.wikipedia.org/wiki/Least_common_multiple )


1.

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HOW THIS SCRIPT WORKS:
In this script  natural numbers starting from the greatest value given is tested simultaneously for divisibility by the given values i.e when finding lcm of 3 and 4 , natural numbers from 4,5,6... are tested  
till lcm is obtained.
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#!/bin/bash

#to find the least common multiple (lcm) of numbers (maximum 9)

#checking whether there is any number provided

if [[ $1 == $null ]];then

    echo -e "\e[1;31mAtleast one number is needed!!\e[0m"

    exit 0

fi 

#for assigning values to array b and finding highest number given 

count=$#

k=1

a=$1

while [[ $# -gt 0 ]];do

    if [[ $1 > $2 ]];then

         a=$1

    fi

b[$k]=$1

k=$k+1

shift

done

#putting values to other positional parameters 

lcm=0

for (( c=9; c>$count; c-- ));do

    b[$c]=1

done 

#finding lcm

for (( i=$a; i>=$a; i++ ));do

    if (( $(($i % ${b[1]})) == 0 && $(($i % ${b[2]})) == 0 && $(($i % ${b[3]})) == 0 && $(($i % ${b[4]})) == 0 && $(($i % ${b[5]})) == 0 && $(($i % ${b[6]})) == 0 && $(($i % ${b[7]})) == 0 && $(($i % ${b[8]})) == 0 && $(($i % ${b[9]})) == 0 ));then

           echo -e "l.c.m = \e[1;34m$i\e[0m"

           exit 0           

    fi

done

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In my system the script is named lcm. To find the lcm of 2 ,6 ,9 and 13 ; in terminal type lcm 2 6 9 13  press enter ..

things I noticed about this script : 
* when more and higher values are given it will take very long time for result
* maximum 9 values only in one calculation  

2.

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HOW THIS SCRIPT WORKS:
Script uses prime factorization method to find lcm. For example for finding lcm of 4 and 6
factors of 4=2 2
factors of 6=2 3
taking common factors only ones and multiplying with all the other factors we get
2x2x3=12
hence lcm=12
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#!/bin/bash

# find lcm of numbers

#usage lcm [number] [number] ...

#checking whether atleast two numbers are provided

if [ "$2" == "$null" ]; then 

    echo -e "\e[1;31mAtleast two numbers required !!\e[0m" 

    exit 0

fi

largestfactor=0

count=1

totalnum=$#

#finding factors of each number and assigning to array factor

#finding largest factor value

while [ $# -gt 0 ];do

     num=$1

     savenum=$1

     for (( i=2; i<=$savenum; i++ ));do

         while [ $((num%$i)) == 0 ];do

             factor[$count]="${factor[$count]} $i"

             if [ $i -gt $largestfactor ];then

                 largestfactor=$i

             fi

             num=$((num/$i))

         done 

     done

     shift

     count=$((count + 1))

done

lcm=1

exponent=0

#finding lcm

for (( i=2; i<=$largestfactor; i++ ));do

    for (( k=1; k<=$totalnum; k++ ));do

        if [[ $(echo ${factor[$k]} | grep -w -o $i | wc -l) -lt $exponent ]];then

             exponent=$(echo ${factor[$k]} | grep -w -o $i | wc -l)

        fi

    done

    lcm=$((lcm*(i**exponent)))

    exponent=0

done

echo -e "l.c.m" = \e[1;34m$lcm\e[0m"

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Usage is same as the first script.


things I noticed about this script : 
* even when more and higher values are given result is obtained fast
* unlimited number of values in one calculation


Enjoy Linux !! 

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