Fomin D.

Find six different natural numbers such that the product of any two of them is divisible by the sum of these two numbers.

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Let's take the numbers $1,2,3,4,5$ and 6. We will compute the least common multiple of 15 sums $1+2,1+3, \ldots, 5+6$. It equals $2^{3 \cdot 3} \cdot 3^{2 \cdot 5 \cdot 7 \cdot 11}=27720$. Multiply the numbers $1,2,3,4,5,6$ by 27720 and we get the desired set.

## Answer

For example, 27720, 55440, 83160, 110880, 138600, 166320.

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