Least Common Multiple Calculator Formula

Understand the math behind the least common multiple calculator. Each variable explained with a worked example.

Formulas Used

Lcm Val

lcm_val = lcm(a, b)

Gcf

gcf = gcd(a, b)

Product

product = a * b

Variables

VariableDescriptionDefault
aFirst Number12
bSecond Number18

How It Works

How to Find the Least Common Multiple

Methods

Method 1: Using GCF

LCM(a, b) = (a × b) / GCF(a, b)

Method 2: Prime Factorization 1. Find the prime factorization of each number 2. Take the highest power of each prime that appears 3. Multiply them together

Method 3: Listing Multiples 1. List multiples of each number 2. Find the smallest number that appears in both lists

Worked Example

Find the LCM of 12 and 18.

a = 12b = 18
  1. 01GCF(12, 18) = 6
  2. 02LCM = (12 × 18) / 6 = 216 / 6 = 36
  3. 03Verification: 36 / 12 = 3 (whole number) and 36 / 18 = 2 (whole number)

Frequently Asked Questions

What is the LCM?

The least common multiple (LCM) is the smallest positive number that is evenly divisible by two or more numbers. For example, LCM(4, 6) = 12.

When do you use the LCM?

The LCM is used when adding or subtracting fractions with different denominators (finding a common denominator), and in problems involving repeating cycles or schedules.

Learn More

Guide

How to Calculate Least Common Multiple (LCM)

Learn how to find the Least Common Multiple (LCM) of two or more numbers using listing multiples, prime factorization, and the GCF formula. Includes step-by-step examples for each method.

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Open Least Common Multiple Calculator