Python program 27 find lcm using while loop in python
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sure! finding the least common multiple (lcm) of two numbers is a common problem in programming. the lcm of two integers is the smallest positive integer that is divisible by both numbers. one way to find the lcm is to use a while loop.
tutorial: finding lcm using while loop in python
#### step-by-step explanation:
1. **understand the concept of lcm**:
the lcm of two numbers, say `a` and `b`, can be found using the formula:
\[
\text{lcm}(a, b) = \frac{|a \times b|}{\text{gcd}(a, b)}
\]
however, since we are instructed to use a while loop, we'll find the lcm by incrementing a multiple of one of the numbers until we find a multiple that is also a multiple of the other number.
2. **initialize variables**:
start with two numbers, `a` and `b`.
initialize a variable to keep track of the multiple of `a` and start with it as `a`.
3. **use a while loop**:
continue looping until you find a number that is divisible by both `a` and `b`.
in each iteration, increment the multiple of `a` by `a`.
4. **return the lcm**:
once you find a number that is divisible by both, that number is the lcm.
#### python code example:
here's a python program that implements the above logic using a while loop:
#### explanation of the code:
**function definition**: the function `find_lcm(a, b)` takes two integers as input.
**input validation**: it checks if either number is non-positive and returns a message if so.
**lcm calculation**: it initializes `lcm` with the value of `a`. the while loop checks if `lcm` is not divisible by `b`. if it isn't, it increases `lcm` by adding `a`.
**return value**: once a number is found that is divisible by both `a` and `b`, it returns that number as the lcm.
**example usage**: the example demonstrates how to call the function and prints the result for the numbers 12 and 15.
#### output:
when you run the code with the example numbers 12 and 15, the output will be:
conclusion:
using a while loop t ...
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