04_Python_Functions_examples/006_find_LCM.ipynb

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    "<small><small><i>\n",
    "All the IPython Notebooks in this **Python Examples** series by Dr. Milaan Parmar are available @ **[GitHub](https://github.com/milaan9/90_Python_Examples)**\n",
    "</i></small></small>"
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    "# Python Program to Find LCM\n",
    "\n",
    "In this example, you'll learn to find the LCM of two numbers and display it.\n",
    "\n",
    "To understand this example, you should have the knowledge of the following **[Python programming](https://github.com/milaan9/01_Python_Introduction/blob/main/000_Intro_to_Python.ipynb)** topics:\n",
    "\n",
    "* **[Python while Loop](https://github.com/milaan9/03_Python_Flow_Control/blob/main/006_Python_while_Loop.ipynb)**\n",
    "* **[Python Functions](https://github.com/milaan9/04_Python_Functions/blob/main/001_Python_Functions.ipynb)**\n",
    "* **[Python Function Arguments](https://github.com/milaan9/04_Python_Functions/blob/main/004_Python_Function_Arguments.ipynb)**\n",
    "* **[Python User-defined Functions](https://github.com/milaan9/04_Python_Functions/blob/main/Python_User_defined_Functions.ipynb)**"
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    "The least common multiple (L.C.M.) of two numbers is the smallest positive integer that is perfectly divisible by the two given numbers.\n",
    "\n",
    "For example, the L.C.M. of 12 and 14 is 84."
   ]
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      "The L.C.M. of 64 and 24 is: 192\n"
     ]
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     "data": {
      "text/plain": [
       "'\\n>>Output/Runtime Test Cases:\\n     \\nThe H.C.F. of 64 and 24 is: 8\\n'"
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    "# Example 1: find the L.C.M. of two input number\n",
    "\n",
    "def compute_lcm(x, y):\n",
    "\n",
    "   # choose the greater number\n",
    "   if x > y:\n",
    "        greater = x\n",
    "   else:\n",
    "        greater = y\n",
    "\n",
    "   while(True):\n",
    "        if((greater % x == 0) and (greater % y == 0)):\n",
    "            lcm = greater\n",
    "            break\n",
    "        greater += 1\n",
    "\n",
    "   return lcm\n",
    "\n",
    "num1 = 64\n",
    "num2 = 24\n",
    "\n",
    "print(\"The L.C.M. of\", num1, \"and\", num2,  \"is:\", compute_lcm(num1, num2))\n",
    "        \n",
    "'''\n",
    ">>Output/Runtime Test Cases:\n",
    "     \n",
    "The H.C.F. of 64 and 24 is: 8\n",
    "'''"
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    "**Explanation:** \n",
    "\n",
    "This program stores two number in **`num1`** and **`num2`** respectively. These numbers are passed to the **`compute_lcm()`** function. The function returns the L.C.M of two numbers.\n",
    "\n",
    "In the function, we first determine the greater of the two numbers since the L.C.M. can only be greater than or equal to the largest number. We then use an infinite **`while`** loop to go from that number and beyond.\n",
    "\n",
    "In each iteration, we check if both the numbers perfectly divide our number. If so, we store the number as L.C.M. and break from the loop. Otherwise, the number is incremented by 1 and the loop continues.\n",
    "\n",
    "The above program is slower to run. We can make it more efficient by using the fact that the product of two numbers is equal to the product of the least common multiple and greatest common divisor of those two numbers.\n",
    "\n",
    "```python\n",
    "Number1 * Number2 = L.C.M. * G.C.D.\n",
    "```\n",
    "\n",
    "Here is a Python program to implement this."
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      "The L.C.M. is: 192\n"
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       "'\\n>>Output/Runtime Test Cases:\\n     \\nThe L.C.M. is: 192\\n'"
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    "# Example 2: find the L.C.M. of two input number\n",
    "\n",
    "# This function computes GCD \n",
    "def compute_gcd(x, y):\n",
    "\n",
    "   while(y):\n",
    "       x, y = y, x % y\n",
    "   return x\n",
    "\n",
    "# This function computes LCM\n",
    "def compute_lcm(x, y):\n",
    "   lcm = (x*y)//compute_gcd(x,y)\n",
    "   return lcm\n",
    "\n",
    "num1 = 64\n",
    "num2 = 24 \n",
    "\n",
    "print(\"The L.C.M. is:\", compute_lcm(num1, num2))\n",
    "\n",
    "'''\n",
    ">>Output/Runtime Test Cases:\n",
    "     \n",
    "The L.C.M. is: 192\n",
    "'''"
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    "**Explanation:** \n",
    "\n",
    "The output of this program is the same as before. We have two functions **`compute_gcd()`** and **`compute_lcm()`**. We require G.C.D. of the numbers to calculate its L.C.M.\n",
    "\n",
    "So, **`compute_lcm()`** calls the function **`compute_gcd()`** to accomplish this. G.C.D. of two numbers can be calculated efficiently using the Euclidean algorithm.\n",
    "\n",
    "Click here to learn more about methods to **[calculate G.C.D in Python](https://github.com/milaan9/90_Python_Examples/blob/main/04_Python_Functions_examples/005_find_HCF_or_GCD.ipynb)**."
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