LCM & GCF Calculator

How this is calculated

Each number is broken down into its prime factors. The GCF is the product of the prime factors shared by every number; the LCM is the product of every prime factor needed by any of the numbers, at its highest power.

LCM and GCF explained

The Least Common Multiple (LCM) is the smallest number that all your numbers divide into evenly. The Greatest Common Factor (GCF, also called GCD) is the largest number that divides evenly into all your numbers — they're opposite ends of the same relationship.

Formula

Example: for 12 and 18, GCF = 6, so LCM = (12 × 18) ÷ 6 = 36.

Quick reference table

Numbers	GCF	LCM
4, 6	2	12
12, 18	6	36
12, 18, 30	6	180

Common pitfalls

• Mixing up LCM and GCF — LCM is always greater than or equal to the largest input number, while GCF is always less than or equal to the smallest.
• Stopping factorization early — a number isn't fully factored until every factor remaining is itself prime.
• Forgetting repeated factors — if a prime appears twice in one number's factorization (like 2×2×3 for 12), it counts twice when comparing to other numbers.

Tips

• For three or more numbers, find the LCM (or GCF) of the first two, then combine that result with the next number, and repeat.
• If two numbers share no prime factors at all, their GCF is 1 and their LCM is simply their product.

Frequently asked questions

What is LCM? LCM stands for Least Common Multiple — the smallest positive number that is a multiple of every number in a given set. The LCM of 4 and 6 is 12.

What is GCF? GCF stands for Greatest Common Factor (also called GCD, Greatest Common Divisor) — the largest number that divides evenly into every number in a given set. The GCF of 12 and 18 is 6.

How do you find the LCM of two numbers? One reliable method: LCM(a, b) = (a × b) ÷ GCF(a, b). For 4 and 6, GCF is 2, so LCM = (4 × 6) ÷ 2 = 12.

How do you find the GCF using prime factorization? Break each number into its prime factors, then multiply together the prime factors common to all the numbers. For 12 (2×2×3) and 18 (2×3×3), the shared factors are 2 and 3, so the GCF is 6.

Why do I need LCM when adding fractions? To add fractions with different denominators, you first convert them to a common denominator — using the LCM of the denominators keeps the numbers as small as possible.

What is the difference between GCF and GCD? GCF (Greatest Common Factor) and GCD (Greatest Common Divisor) are two names for exactly the same value — different textbooks and regions prefer one term or the other.

Worked examples

Example 1 — Two numbers: 4 and 6 → GCF = 2, LCM = 12.

Example 2 — Adding fractions: to add 1/12 + 1/18, find the LCM of 12 and 18 (which is 36) as the common denominator: 3/36 + 2/36 = 5/36.

Example 3 — Three numbers: 12, 18, and 30 → GCF = 6, LCM = 180.

Where LCM and GCF are useful

Problems that use the LCM

Two buses leave a stop every 12 and 18 minutes. They next leave together after the least common multiple of 12 and 18, which is 36 minutes. LCM is the key idea behind repeating schedules, rotating shifts and finding a common denominator.

Problems that use the GCF

To cover a 24 by 36 inch panel with identical square tiles and no cutting, the largest tile has a side equal to the GCF of 24 and 36, which is 12 inches. GCF is also how you reduce fractions to lowest terms.

A relationship worth remembering

For 12 and 18, GCF is 6, so the LCM is 12 × 18 ÷ 6 = 36. This shortcut works for two numbers and saves effort when the GCF is easy to find.

More questions

Can the LCM be smaller than one of the numbers? No. The LCM is always at least as large as the biggest number in the group.

What if the numbers share no factors? Their GCF is 1, and their LCM is simply their product.