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 * bVariables
| Variable | Description | Default |
|---|---|---|
a | First Number | 12 |
b | Second Number | 18 |
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.
- 01GCF(12, 18) = 6
- 02LCM = (12 × 18) / 6 = 216 / 6 = 36
- 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.
Ready to run the numbers?
Open Least Common Multiple Calculator