- #1

Mr Davis 97

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## Homework Statement

All of the divisors of ##n## are in increasing order: ##1=d_1 < d_2 < \dots < d_t = n##. We know that ##d_6=15##. What is the smallest possible value of ##n##?

## Homework Equations

## The Attempt at a Solution

Here is my reasoning. We have the chain ##1 < d_2 < d_3 < d_4 < d_5 < 15 < n##, where we make ##15## the largest factor that's not ##n##. Since ##15~|~n##, we have that ##5~|~n## and ##3~|~n##. Hence, we have to put ##3## and ##5## somewhere. The minimal sequence is then ##1 < 2 < 3 < 4 < 5 < 15 < n##, so ##n=2\cdot 3\cdot 4 \cdot 5 \cdot 15 =1800##