{"id":10017,"date":"2021-09-30T17:30:51","date_gmt":"2021-09-30T12:00:51","guid":{"rendered":"https:\/\/python-programs.com\/?p=10017"},"modified":"2021-11-22T18:33:31","modified_gmt":"2021-11-22T13:03:31","slug":"python-program-to-find-the-lcm-of-two-numbers-using-recursion","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-to-find-the-lcm-of-two-numbers-using-recursion\/","title":{"rendered":"Python Program to Find the LCM of Two Numbers Using Recursion"},"content":{"rendered":"<p>Practice Java programming from home without using any fancy software just by tapping on this <a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\">Simple Java Programs for Beginners<\/a> tutorial.<\/p>\n<p><strong>Recursion:<\/strong><\/p>\n<p>Recursion is a functional technique to problem-solving that involves breaking an issue down into a series of small subproblems with an identical pattern and solving them sequentially by calling one subproblem within another. Recursion is carried out by defining a function capable of solving one subproblem at a time. It calls itself but solves another subproblem somewhere inside that method. As a result, the call to itself continues until some limiting requirements are met.<\/p>\n<p>The main program&#8217;s first call to a recursive function will be returned only after all sub calls have completed. As a result, Python keeps the results of all subproblems in temporary memory, does some arithmetic operations (if necessary), and releases the memory at the end of the recursion.<\/p>\n<p>The smallest positive number that is divisible by both a and b is the least or lowest common multiple (LCM) of two numbers a and b. In this article, we&#8217;ll look at how to use recursion to find the LCM of two numbers.<\/p>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>given first number = 10\r\ngiven second number = 16<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The value of lcm of the given two numbers 10 16  =  80<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>given first number = 10\r\ngiven second number = 16<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The value of lcm of the given two numbers 5 17  =  85<\/pre>\n<h2>Program to Find the LCM of Two Numbers Using Recursion in Python<\/h2>\n<p>There are several ways to calculate the lcm of the given two numbers using recursion some of them are:<\/p>\n<ul>\n<li><a href=\"#Using_Recursion_(Static_Input)\">Using Recursion (Static Input)<\/a><\/li>\n<li><a href=\"#Using_Recursion_(User_Input_separated_by_space)\">Using Recursion (User Input separated by space)<\/a><\/li>\n<li><a href=\"#Using_Recursion_(User_Input_separated_by_newline)\">Using Recursion (User Input separated by newline)<\/a><\/li>\n<\/ul>\n<h3 id=\"Using_Recursion_(Static_Input)\">Method #1:Using Recursion (Static Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Give two numbers as static input and store them in two variables.<\/li>\n<li>Pass the given two numbers as arguments to the recursive function which calculates the lcm of the given two numbers.<\/li>\n<li>Set the multiple variable to the highest value between the given two numbers.<\/li>\n<li>Check to see if the multiple variable\u00a0 divides both given numbers perfectly.<\/li>\n<li>If it does, the process is terminated and the multiple variable is returned as the LCM.<\/li>\n<li>If the multiple does not divide both given numbers perfectly, then it is increased by the maximum value among both given numbers using the max() function.<\/li>\n<li>The recursive function returns the multiple variable which is the result(lcm of the given two numbers)<\/li>\n<li>Print the LCM of the given two numbers.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># function which accepts the given two numbers as arguments\r\n# and return the lcm of the given two numbers.\r\n\r\n\r\ndef lcmRecursion(numb1, numb2):\r\n    # Set the multiple variable to the highest value between the given two numbers.\r\n    lcmRecursion.multiple = lcmRecursion.multiple+numb2\r\n    # Check to see if the multiple variable\u00a0 divides both given numbers perfectly.\r\n    if((lcmRecursion.multiple % numb1 == 0) and (lcmRecursion.multiple % numb2 == 0)):\r\n      # If it does, the process is terminated and the multiple variable is returned as the LCM.\r\n        return lcmRecursion.multiple\r\n    else:\r\n      # If the multiple does not divide both given numbers perfectly, then it is increased by the maximum value\r\n      # among both given numbers using the max() function.\r\n        lcmRecursion(numb1, numb2)\r\n    # The recursive function returns the multiple variable\r\n    # which is the result(lcm of the given two numbers)\r\n    return lcmRecursion.multiple\r\n\r\n\r\n# set multiplee variable value to 0\r\nlcmRecursion.multiple = 0\r\n# Give two numbers as static input and store them in two variables.\r\nnumbe1 = 10\r\nnumbe2 = 16\r\n# if the first number is greater than second number then swap the arguments\r\nif(numbe1 &gt; numbe2):\r\n    LcmVal = lcmRecursion(numbe2, numbe1)\r\n# else pass the original numbers as arguments\r\nelse:\r\n    LcmVal = lcmRecursion(numbe1, numbe2)\r\nprint('The value of lcm of the given two numbers', numbe1, numbe2, ' = ', LcmVal)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The value of lcm of the given two numbers 10 16  =  80<\/pre>\n<p><strong>Explanation:<\/strong><\/p>\n<ul>\n<li>The two numbers are given as static input.<\/li>\n<li>The multiple variable is set to the highest value between the given two numbers.<\/li>\n<li>The multiple variable is tested to see if it divides the given two numbers perfectly.<\/li>\n<li>If so, the procedure is terminated and the multiple is returned as the LCM.<\/li>\n<li>If the multiple variable does not divide the given two numbers perfectly, the multiple variable is returned by the maximum value among both given numbers.<\/li>\n<li>The variable with multiple values is returned, and the LCM of the two variables is printed.<\/li>\n<\/ul>\n<h3 id=\"Using_Recursion_(User_Input_separated_by_space)\">Method #2:Using Recursion (User Input separated by space)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Scan the given two numbers as user input using a map, int, and split() functions and store them in two variables.<\/li>\n<li>Pass the given two numbers as arguments to the recursive function which calculates the lcm of the given two numbers.<\/li>\n<li>Set the multiple variable to the highest value between the given two numbers.<\/li>\n<li>Check to see if the multiple variable divides both given numbers perfectly.<\/li>\n<li>If it does, the process is terminated and the multiple variable is returned as the LCM.<\/li>\n<li>If the multiple does not divide both given numbers perfectly, then it is increased by the maximum value among both given numbers using the max() function.<\/li>\n<li>The recursive function returns the multiple variable which is the result(lcm of the given two numbers)<\/li>\n<li>Print the LCM of the given two numbers.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># function which accepts the given two numbers as arguments\r\n# and return the lcm of the given two numbers.\r\n\r\n\r\ndef lcmRecursion(numb1, numb2):\r\n    # Set the multiple variable to the highest value between the given two numbers.\r\n    lcmRecursion.multiple = lcmRecursion.multiple+numb2\r\n    # Check to see if the multiple variable\u00a0 divides both given numbers perfectly.\r\n    if((lcmRecursion.multiple % numb1 == 0) and (lcmRecursion.multiple % numb2 == 0)):\r\n      # If it does, the process is terminated and the multiple variable is returned as the LCM.\r\n        return lcmRecursion.multiple\r\n    else:\r\n      # If the multiple does not divide both given numbers perfectly, then it is increased by the maximum value\r\n      # among both given numbers using the max() function.\r\n        lcmRecursion(numb1, numb2)\r\n    # The recursive function returns the multiple variable\r\n    # which is the result(lcm of the given two numbers)\r\n    return lcmRecursion.multiple\r\n\r\n\r\n# set multiplee variable value to 0\r\nlcmRecursion.multiple = 0\r\n# Scan the given two numbers as user input using a map,\r\n# int, and split() functions and store them in two variables.\r\nnumbe1, numbe2 = map(int, input(\r\n    'Enter two random numbers separated by space =').split())\r\n# if the first number is greater than second number then swap the arguments\r\nif(numbe1 &gt; numbe2):\r\n    LcmVal = lcmRecursion(numbe2, numbe1)\r\n# else pass the original numbers as arguments\r\nelse:\r\n    LcmVal = lcmRecursion(numbe1, numbe2)\r\nprint('The value of lcm of the given two numbers', numbe1, numbe2, ' = ', LcmVal)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter two random numbers separated by space =5 17\r\nThe value of lcm of the given two numbers 5 17 = 85\r\n<\/pre>\n<p><strong>Explanation:<\/strong><\/p>\n<pre>Here the map function converts the given two numbers from string to integer data type and the split() function\r\nsplits the given two numbers by space.<\/pre>\n<h3 id=\"Using_Recursion_(User_Input_separated_by_newline)\">Method #3:Using Recursion (User Input separated by newline)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Scan the first number as user input using the int(input()) function and store it in a\u00a0 variable.<\/li>\n<li>Scan the second number as user input using the int(input()) function and store it in another variable.<\/li>\n<li>Here int() is used to convert the given number to integer datatype.<\/li>\n<li>Pass the given two numbers as arguments to the recursive function which calculates the lcm of the given two numbers.<\/li>\n<li>Set the multiple variable to the highest value between the given two numbers.<\/li>\n<li>Check to see if the multiple variable divides both given numbers perfectly.<\/li>\n<li>If it does, the process is terminated and the multiple variable is returned as the LCM.<\/li>\n<li>If the multiple does not divide both given numbers perfectly, then it is increased by the maximum value among both given numbers using the max() function.<\/li>\n<li>The recursive function returns the multiple variable which is the result(lcm of the given two numbers)<\/li>\n<li>Print the LCM of the given two numbers.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># function which accepts the given two numbers as arguments\r\n# and return the lcm of the given two numbers.\r\n\r\n\r\ndef lcmRecursion(numb1, numb2):\r\n    # Set the multiple variable to the highest value between the given two numbers.\r\n    lcmRecursion.multiple = lcmRecursion.multiple+numb2\r\n    # Check to see if the multiple variable\u00a0 divides both given numbers perfectly.\r\n    if((lcmRecursion.multiple % numb1 == 0) and (lcmRecursion.multiple % numb2 == 0)):\r\n      # If it does, the process is terminated and the multiple variable is returned as the LCM.\r\n        return lcmRecursion.multiple\r\n    else:\r\n      # If the multiple does not divide both given numbers perfectly, then it is increased by the maximum value\r\n      # among both given numbers using the max() function.\r\n        lcmRecursion(numb1, numb2)\r\n    # The recursive function returns the multiple variable\r\n    # which is the result(lcm of the given two numbers)\r\n    return lcmRecursion.multiple\r\n\r\n\r\n# set multiplee variable value to 0\r\nlcmRecursion.multiple = 0\r\n# Scan the first number as user input using the int(input())\r\n# function and store it in a\u00a0 variable.\r\nnumbe1 = int(input('Enter some random number = '))\r\n# Scan the second number as user input using the int(input())\r\n# function and store it in another variable.\r\n# Here int() is used to convert the given number to integer datatype.\r\nnumbe2=int(input('Enter some random number = '))\r\n# if the first number is greater than second number then swap the arguments\r\nif(numbe1 &gt; numbe2):\r\n    LcmVal=lcmRecursion(numbe2, numbe1)\r\n# else pass the original numbers as arguments\r\nelse:\r\n    LcmVal=lcmRecursion(numbe1, numbe2)\r\nprint('The value of lcm of the given two numbers', numbe1, numbe2, ' = ', LcmVal)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter some random number = 9\r\nEnter some random number = 3\r\nThe value of lcm of the given two numbers 9 3 = 9<\/pre>\n<p><strong>Related Programs<\/strong>:<\/p>\n<ul>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-check-whether-a-string-is-a-palindrome-or-not-using-recursion\/\">Python Program to Check Whether a String is a Palindrome or not Using Recursion<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-the-product-of-two-numbers-using-recursion\/\">Python Program to Find the Product of two Numbers Using Recursion<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-if-a-number-is-prime-or-not-prime-using-recursion\/\">Python Program to Find if a Number is Prime or Not Prime Using Recursion<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-the-power-of-a-number-using-recursion\/\">Python Program to Find the Power of a Number Using Recursion<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-the-length-of-a-list-using-recursion\/\">Python Program to Find the Length of a List Using Recursion<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-reverse-a-string-using-recursion\/\">Python Program to Reverse a String Using Recursion<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Practice Java programming from home without using any fancy software just by tapping on this Simple Java Programs for Beginners tutorial. 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