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Шаг за шагом

1. \gcd(4, 6)

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

2. 6 = 1 \times 4 + 2

   Divide 6 by 4: quotient 1, remainder 2.

3. 4 = 2 \times 2 + 0

   Divide 4 by 2: quotient 2, remainder 0.

4. \gcd(4, 6) = 2

   Euclid gives the gcd.

5. \operatorname{lcm}(4, 6) = \frac{4 \times 6}{\gcd(4, 6)} = \frac{24}{2} = 12

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