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1. \gcd(12, 18)

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

2. 18 = 1 \times 12 + 6

   Divide 18 by 12: quotient 1, remainder 6.

3. 12 = 2 \times 6 + 0

   Divide 12 by 6: quotient 2, remainder 0.

4. \gcd(12, 18) = 6

   Euclid gives the gcd.

5. \operatorname{lcm}(12, 18) = \frac{12 \times 18}{\gcd(12, 18)} = \frac{216}{6} = 36

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