OlympiadEasyNumber Theory7–9

A whole number is divisible by $4$ and also by $6$ . Which of these numbers must it always be divisible by?

Um número inteiro é divisível por $4$ e também por $6$ . Por qual destes números é que ele tem obrigatoriamente de ser divisível?

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Solution

The guaranteed divisor is the least common multiple, $\text{lcm}(4, 6) = 12$ , not the product $24$ : for instance $12$ itself is divisible by $4$ and $6$ but not by $24$ , by $8$ or by $18$ .

A whole number is divisible by 444 and also by 666. Which of these numbers must it always be divisible by?

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A whole number is divisible by $4$ and also by $6$ . Which of these numbers must it always be divisible by?