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LCM Calculator

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Number 2

Least Common Multiple

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Reviewed by Dr. Alex M., Ph.D.

Last updated: November 2025

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💡 Expert Tips

Use the GCD Shortcut

Instead of listing multiples, use this formula: LCM(a, b) = (a × b) / GCD(a, b). It's much faster, especially for large numbers!

LCD = LCM of Denominators

To add 1/4 + 1/6, find LCM(4, 6) = 12. That's your Least Common Denominator. Convert: 3/12 + 2/12 = 5/12.

Timing Problems

If two events repeat every 4 and 6 days, they coincide again after LCM(4, 6) = 12 days. LCM solves "when will they sync up?" problems.

⚠️ Common Mistakes

Confusing LCM with GCD

LCM is the SMALLEST multiple. GCD is the LARGEST divisor. LCM is usually bigger than both numbers. GCD is usually smaller.

Just Multiplying the Numbers

LCM(12, 18) ≠ 216. The LCM is 36, not 12 × 18. Always simplify using GCD first.

Special Case: LCM(a, 0)

By definition, LCM(a, 0) = 0 because 0 is divisible by everything. Don't assume it's 'a'.

❓ Frequently Asked Questions

What is LCM? +

LCM (Least Common Multiple) is the smallest positive integer that is divisible by both numbers. For example, LCM(4, 6) = 12 because 12 is the smallest number that both 4 and 6 divide into evenly.

How do you calculate LCM? +

The most efficient method is: LCM(a, b) = (a × b) / GCD(a, b). First find the GCD using the Euclidean algorithm, then use this formula.

What is the LCM of two prime numbers? +

The LCM of two different prime numbers is their product. For example, LCM(3, 5) = 15 because prime numbers have no common factors.

Why is LCM useful for fractions? +

To add or subtract fractions with different denominators, you need a common denominator. The LCM of the denominators gives you the least (smallest) common denominator.

What is the difference between LCM and GCD? +

LCM is the smallest number that both divide into, while GCD is the largest number that divides both. They are opposites: LCM(a,b) × GCD(a,b) = a × b.