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LCM Calculator

Find the Least Common Multiple (LCM) of two or three numbers with clear mathematical steps, prime factorization listing, and multiples comparisons.

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Interactive LCM Calculator Workspace

Live Solver
Least Common MultipleLCM = 60

LCM Derivation

Find Least Common Multiple using the formula: LCM(a, b) = (|a × b|) / GCF(a, b)
Step 1: Compute product of the two numbers: 12 × 15 = 180
Step 2: Find the GCF of 12 and 15 (which is 3).
> Start with Euclidean algorithm for 12 and 15:
> 12 = (15 × 0) + 12 (Remainder: 12)
> 15 = (12 × 1) + 3 (Remainder: 3)
> 12 = (3 × 4) + 0 (Remainder: 0)
> The last non-zero remainder is 3.
Step 3: Divide product by GCF: 180 ÷ 3 = 60.

Mathematical Formula & Variables

Equation ModelLCM(a, b) = |a × b| / GCF(a, b) | LCM(a, b, c) = LCM(LCM(a, b), c)

The LCM is computed by dividing the absolute product of two numbers by their Greatest Common Factor (GCF). For three numbers, find the LCM of the first two and then find the LCM of that result and the third.

Variable Definitions

SymbolDescription
a, b, cThe positive integers for which you are calculating the LCM
GCF(a, b)The Greatest Common Factor of the inputs

How to Use the LCM Calculator

  • Enter two or three positive integers in the input fields.
  • Click calculate to output the LCM.
  • View the prime factor exponential comparison or list of common multiples.

Practical Example Calculation

Scenario Context: Finding the LCM of 12 and 15.

Step 1: Find the GCF of 12 and 15: GCF is 3.
Step 2: Multiply the two numbers: 12 × 15 = 180.
Step 3: Divide product by GCF: 180 ÷ 3 = 60.
The LCM of 12 and 15 is 60.

Frequently Asked Questions

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