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What is the sum of all positive integers r  that satisfy

lcm [ r, 700 ] = 7000

#1
0

If you were thinking of the LCM[10,700], it doesn't equal 7,000, but 700!.

Guest Apr 13, 2018
#2
+20680
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What is the sum of all positive integers r  that satisfy

lcm [ r, 700 ] = 7000

factorization

$$\begin{array}{|rcll|} \hline lcm [ r, 2^2\times 5^2\times 7^1] &=& 2^3\times 5^3 \times 7^1 \\\\ r &=& 2^3\times 5^3 \times 7^0 & = 1000 \\ r &=& 2^3\times 5^3 \times 7^1 & = 7000 \\ sum &=& & =8000 \\ \hline \end{array}$$

The sum of all positive integers r is 8000

heureka  Apr 13, 2018