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1. \gcd(2, 3)

   Use Euclid's algorithm: replace the larger number by its remainder on division by the smaller, until the remainder is 0.

2. 3 = 1 \times 2 + 1

   Divide 3 by 2: quotient 1, remainder 1.

3. 2 = 2 \times 1 + 0

   Divide 2 by 1: quotient 2, remainder 0.

4. \gcd(2, 3) = 1

   Euclid gives the gcd.

5. \operatorname{lcm}(2, 3) = \frac{2 \times 3}{\gcd(2, 3)} = \frac{6}{1} = 6

   lcm × gcd = a × b, so divide the product by the gcd.