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LCM Calculator

Use this free online LCM calculator to find the Least Common Multiple of two or more numbers. Enter your values and get the result instantly with step-by-step explanation.

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Formula

LCM(a, b) = |a × b| / GCD(a, b)

Multiply the two numbers, then divide by their greatest common divisor to find the LCM.

Worked Example

Find LCM of 12 and 18 Step 1: GCD(12, 18) = 6 Step 2: LCM = |12 × 18| / 6 = 216 / 6 = 36 Result: LCM = 36

What Is the Least Common Multiple (LCM)?

The Least Common Multiple of two numbers is the smallest positive integer that is evenly divisible by both numbers. LCM is closely related to the GCD (Greatest Common Divisor) and is used whenever you need to find a common ground between two cyclic or repeating quantities.
  • LCM(4, 6) = 12 because 12 is the smallest number divisible by both 4 and 6
  • LCM is essential for adding fractions: to add 1/4 + 1/6, you need the LCM of 4 and 6 (which is 12)
  • The relationship LCM(a,b) x GCD(a,b) = a x b provides an efficient way to calculate LCM
  • LCM of any number with itself is the number itself, and LCM of any number with 1 is that number

LCM is used in fraction arithmetic, scheduling problems (when do two events coincide again?), gear ratios, and tiling patterns.

You can also calculate changes using our GCD Calculator or Fraction Calculator.

Frequently Asked Questions

What is the LCM?

The Least Common Multiple is the smallest positive integer that is divisible by both numbers. For example, LCM(3, 5) = 15 because 15 is the smallest number evenly divisible by both 3 and 5.

When is LCM useful?

Finding common denominators for fractions, scheduling problems (e.g., two buses arriving at the same stop at different intervals), and determining when cyclic patterns align.

How is LCM related to GCD?

LCM(a,b) x GCD(a,b) = a x b. This means if you know the GCD, you can quickly calculate the LCM by dividing the product of the two numbers by their GCD.

How do I find the LCM of more than two numbers?

Find the LCM of the first two numbers, then find the LCM of that result with the third number, and so on. For example, LCM(4, 6, 10): LCM(4,6) = 12, then LCM(12, 10) = 60.

Can the LCM be smaller than either number?

No. The LCM is always at least as large as the larger of the two numbers. The smallest possible LCM is when one number divides the other (e.g., LCM(3, 6) = 6).

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