Python: Least Common Multiple (LCM) of more than two numbers

Python Basic - 1: Exercise-135 with Solution

Write a Python program that calculates the Least Common Multiple (LCM) of more than two numbers. The numbers should be taken from a given list of positive integers.

From Wikipedia,
In arithmetic and number theory, the least common multiple, 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 divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero. However, some authors define lcm(a,0) as 0 for all a, which is the result of taking the lcm to be the least upper bound in the lattice of divisibility.

Sample Solution-1:

Python Code:

from functools import reduce
def test(nums):
    return reduce(lambda x,y:lcm(x,y),nums)
def gcd(a, b):
    while b:
        a, b = b, a%b
    return a
def lcm(a, b):
    return a*b // gcd(a, b)
nums = [ 4, 6, 8 ]
print("Original list elements:")
print(nums)
print("LCM of the numbers of the said array of positive integers: ", test(nums))
nums = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
print("\nOriginal list elements:")
print(nums)
print("LCM of the numbers of the said array of positive integers: ", test(nums))
nums = [ 48, 72, 108  ]
print("\nOriginal list elements:")
print(nums)
print("LCM of the numbers of the said array of positive integers: ", test(nums))

Sample Output:

Original list elements:
[4, 6, 8]
LCM of the numbers of the said array of positive integers:  24

Original list elements:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
LCM of the numbers of the said array of positive integers:  2520

Original list elements:
[48, 72, 108]
LCM of the numbers of the said array of positive integers:  432

Flowchart:

Sample Solution-2:

Use functools.reduce(), math.gcd() and lcm(x,y) = x * y / gcd(x,y) over the given list.

Python Code:

from functools import reduce
from math import gcd

def lcm(numbers):
  return reduce((lambda x, y: int(x * y / gcd(x, y))), numbers)

print(lcm([ 4, 6, 8 ]))  
print(lcm([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])) 
print(lcm([48, 72, 108]))  

Sample Output:

24
2520
432

Flowchart:

Visualize Python code execution:

The following tool visualize what the computer is doing step-by-step as it executes the said program:

Python Code Editor:

Have another way to solve this solution? Contribute your code (and comments) through Disqus.

Previous: Write a Python program to alternate the case of each letter in a given string and the first letter of the said string must be uppercase.
Next: Write a Python program to reverse all the words which have odd length.