Mathematics CalcyZone Calculator

LCM Calculator (Least Common Multiple)

Find the least common multiple (LCM) of two or more numbers.

Number 1

Number 2

Calculation Solution

LCM = 300

GCD of numbers: 50

Mathematical Formula

LCM(a, b) = (|a * b|) / GCD(a, b)

Overview & Explanation

The Least Common Multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers without remainder.

How It Works

Find the greatest common divisor (GCD) of the two numbers.
Multiply the two numbers and divide by GCD.

Practical Applications

Finding common denominators for fraction addition.
Scheduling recurring events.

Least common multiple

The least common multiple (LCM) of two or more whole numbers is the smallest positive number that each of them divides into exactly. For 12 and 18, the multiples of 12 are 12, 24, 36, 48… and of 18 are 18, 36, 54…, so the LCM is 36.

Methods

Prime factorisation is reliable for any size: 12 = 2² × 3 and 18 = 2 × 3². Take each prime at its highest power: 2² × 3² = 36.

A faster method uses the greatest common divisor: LCM(a, b) = a × b ÷ GCD(a, b). Since GCD(12, 18) = 6, LCM = 216 ÷ 6 = 36. For more than two numbers, work in pairs: LCM(4, 6, 10) = LCM(LCM(4, 6), 10) = LCM(12, 10) = 60.

Where the LCM is used

The LCM gives the lowest common denominator when adding fractions: to add 1/12 and 1/18, rewrite both over 36 as 3/36 + 2/36 = 5/36. It also answers timing questions: if one bus leaves every 12 minutes and another every 18 minutes, and both leave together at 9:00, they next leave together 36 minutes later, at 9:36. Gear teeth, repeating schedules and tiling patterns use the same idea.