Numbers

Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17.

What is its sum?

Correct answer:

n =  1212
S =  2536754178

Step-by-step explanation:

$$\begin{gathered} a_1=29\cdot 7\cdot 17=3451 \\ n=\lfloor {\displaystyle \frac{4183444}{a_1}}\rfloor =1212 \end{gathered}$$

$S={\displaystyle \frac{n}{2}}(a_1+a_n)={\displaystyle \frac{n}{2}}(a_1+n{a}_1)={\displaystyle \frac{n(n+1)}{2}}\cdot a_1=2536754178$

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