Python math.lcm() Function

Python math 模块Python math Module

In number theory,the least common multiple(Least Common Multiple, abbreviated as LCM) is a very important concept. It is used to find the smallest among the common multiples of two or more integers.

math.lcm()is a function introduced in Python 3.9, specifically used to calculate theLeast Common Multiple (LCM)。

Term Explanation： lcmis the abbreviation of "Least Common Multiple", meaning "least common multiple".

Basic Syntax and Parameters

Syntax Format

import math

math.lcm(*integers)

Parameter Description

  • Parameter： *integers- Variable number of integers (at least one)
  • Description: The integers for which to calculate the least common multiple.

Return Value

  • Returns the least common multiple of all input integers
  • If only one integer is passed, returns the absolute value of that integer
  • If 0 is passed, returns 0

Examples

Example 1: Basic Usage - Calculating LCM of Two Numbers

Example

import math

print("LCM of 4 and 6:", math.lcm(4, 6))     # 12
print("LCM of 5 and 7:", math.lcm(5, 7))     # 35
print("LCM of 12 and 18:", math.lcm(12, 18)) # 36

# Verify the formula
a, b = 4, 6
print(f"\n"Verify: LCM({a}, {b}) = {a} * {b} / GCD({a}, {b}) = {a*b//math.gcd(a,b)}")

Run result:

4 和 6 的 LCM: 12
5 和 7 的 LCM: 35
12 和 18 的 LCM: 36

验证: LCM(4, 6) = 4 * 6 / GCD(4, 6) = 12

Example 2: Calculating LCM of Multiple Numbers

Example

import math

print("LCM of 3, 4, 5:", math.lcm(3, 4, 5))    # 60
print("LCM of 6, 8, 12:", math.lcm(6, 8, 12))  # 24
print("LCM of 2, 3, 4, 5:", math.lcm(2, 3, 4, 5)) # 60

Run result:

3, 4, 5 的 LCM: 60
6, 8, 12 的 LCM: 24
2, 3, 4, 5 的 LCM: 60

Example 3: Handling Special Values

Example

import math

print("Single integer 7:", math.lcm(7))
print("LCM of 0 and 5:", math.lcm(0, 5))
print("LCM of -4 and 6:", math.lcm(-4, 6))

Run result:

单个整数 7: 7
0 和 5 的 LCM: 0
-4 和 6 的 LCM: 12

Example 4: Practical Application - Fraction Reduction to a Common Denominator

Example

import math

# Fraction addition: 1/4 + 1/6
denom1, denom2 = 4, 6
common_denom = math.lcm(denom1, denom2)
numer1 = 1 * (common_denom // denom1)
numer2 = 1 * (common_denom // denom2)
result = numer1 + numer2
print(f"1/{denom1} + 1/{denom2} = {numer1}/{common_denom} + {numer2}/{common_denom} = {result}/{common_denom}")

Run result:

1/4 + 1/6 = 3/12 + 2/12 = 5/12

Example 5: Practical Application - Cycle Synchronization

Example

import math

# The periods of three traffic lights are 30, 45, and 60 seconds
light_cycles = [30, 45, 60]
sync_interval = math.lcm(*light_cycles)
print(f"Traffic light periods: {light_cycles}")
print(f"Time interval for turning green simultaneously: {sync_interval} seconds")

Run result:

信号灯周期: [30, 45, 60]
同时变绿的时间间隔: 180 秒

Relationship with GCD

Formula: LCM(a, b) = a × b / GCD(a, b)

Example

import math

for a, b in [(4, 6), (8, 12), (15, 20)]:
    lcm_val = math.lcm(a, b)
    gcd_val = math.gcd(a, b)
    print(f"LCM({a}, {b}) = {lcm_val}, GCD({a}, {b}) = {gcd_val}, Verify: {lcm_val * gcd_val} == {a*b} -> {lcm_val*gcd_val == a*b}")

Run result:

LCM(4, 6) = 12, GCD(4, 6) = 2, 验证: 24 == 24 -> True
LCM(8, 12) = 24, GCD(8, 12) = 4, 验证: 96 == 96 -> True
LCM(15, 20) = 60, GCD(15, 20) = 5, 验证: 300 == 300 -> True

Notes

  • math.lcm()Only available in Python 3.9+
  • Negative numbers are calculated using their absolute values
  • The LCM of 0 and any number is 0

Python math 模块Python math Module

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