LCM of two numbers in Python

The least common multiple (LCM) of two numbers is the smallest positive number that both of them divide into. The LCM of 4 and 6 is 12. It is what you need to add fractions like 1/4 + 1/6.

The program

import math


def lcm(a, b):
    if a == 0 or b == 0:
        return 0
    return abs(a * b) // math.gcd(a, b)


print("LCM of 4 and 6 =", lcm(4, 6))
print("LCM of 21 and 6 =", lcm(21, 6))
print("LCM of 7 and 5 =", lcm(7, 5))

LCM of 4 and 6 = 12
LCM of 21 and 6 = 42
LCM of 7 and 5 = 35

How it works

• For two positive numbers, GCD × LCM = a × b. So the LCM is a * b divided by the GCD.
• For 21 and 6: the GCD is 3, so the LCM is 126 // 3 = 42.
• // (floor division) keeps the result a whole number. The division is always exact here, so nothing is lost.
• abs() keeps the result positive for negative input.
• The check for zero comes first: by convention the LCM with 0 is 0, and math.gcd(0, 0) is 0, so the division would raise a ZeroDivisionError.

The GCD program shows how the GCD itself is calculated.

Another way: math.lcm()

Python 3.9 added math.lcm(). It accepts any number of values:

import math

print(math.lcm(4, 6))
print(math.lcm(4, 6, 10))
print(math.lcm(0, 5))

12
60
0

The LCM of 4, 6 and 10 is 60: buses that leave every 4, 6 and 10 minutes all leave together again after 60 minutes.