Least Common Multiple Calculator Formula

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

Use the Least Common Multiple Calculator

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)

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