LCM Calculator

Free online LCM Calculator with step-by-step solutions. 100% client-side, no data upload.

⌘/Ctrl + Enter to calculate · live updates as you type

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LCM Calculator

This free online LCM calculator computes the Least Common Multiple of two or more positive integers instantly in your browser, with no signup, no ads, and no server uploads.

What is the Least Common Multiple? The Least Common Multiple of two integers $a$ and $b$, denoted by $\operatorname{lcm}(a, b)$, is the smallest positive integer that is divisible by both $a$ and $b$. For example, $\operatorname{lcm}(15, 25) = 75$ because 75 is the smallest number divisible by both 15 and 25.

The LCM is closely related to the Greatest Common Factor (GCF):

$$\operatorname{lcm}(a, b) \times \gcd(a, b) = a \times b$$

This gives us a convenient formula: $\operatorname{lcm}(a, b) = \frac{a \times b}{\gcd(a, b)}$.

Prime Factorization Method Each number is expressed as a product of its prime factors. The LCM takes each prime factor with the highest exponent that appears:

$15 = 3 \times 5$ $25 = 5^2$ $\operatorname{lcm}(15, 25) = 3 \times 5^2 = 75$

Listing Multiples Method List multiples of each number:

Multiples of 15: 15, 30, 45, 60, 75, ... Multiples of 25: 25, 50, 75, 100, ... The first common multiple is 75.

GCF Formula Method Using the relationship $\operatorname{lcm}(a, b) = \frac{a \times b}{\gcd(a, b)}$:

For 15 and 25: $\gcd(15, 25) = 5$, so $\operatorname{lcm}(15, 25) = 15 \times 25 \div 5 = 75$.

Applications LCM is used for: - Adding and subtracting fractions (Least Common Denominator) - Scheduling events and timekeeping - Gear ratio calculations in mechanical engineering - Music theory and rhythmic patterns - Solving word problems about repeating cycles
How to use this calculator Enter two or more positive integers separated by commas. The LCM is computed and displayed instantly, along with the GCF, the relationship between them, and the first 10 common multiples. The step-by-step section shows prime factorization, listing multiples, and the GCF formula.

The calculation updates live as you type with a short debounce. You can also click Calculate or press Ctrl+Enter.

Privacy & Performance All calculations run locally in your browser. No data is transmitted, logged, or stored on any server.
🔒 Client-side only⚡ Web Worker processing🌐 Works offline🛡️ Zero server logs

Frequently Asked Questions

Got questions about LCM? We've got answers.

What is LCM used for?

LCM is primarily used for adding and subtracting fractions with different denominators — it provides the Least Common Denominator. It is also used in scheduling problems, gear ratio calculations, and any scenario where you need to find when events with different cycles coincide.

What is the difference between LCM and GCF?

The LCM (Least Common Multiple) is the smallest number divisible by both given numbers. The GCF (Greatest Common Factor) is the largest number that divides both given numbers. They are related by the formula: LCM × GCF = a × b.

Can LCM be used for more than two numbers?

Yes. To find the LCM of three or more numbers, compute the LCM of the first two numbers, then compute the LCM of that result with the next number, and continue until all numbers have been processed.

Is this calculator private?

Yes. All calculations run locally in your browser. No data is transmitted or stored on any server.

Can I use this on mobile?

Yes, the tool works on all devices with a modern browser.