\(n_x= 10n_0– 1\)
\(\frac{n_x}{n_0}= 10– \frac{1}{n_0}\)
since \(n_0\) is a positive integer, \(9<=10– \frac{1}{n_0} <10\)
Hence, values of \([\frac{n_0}{n_0}]\), \([\frac{n_1}{n_0}]\), \([\frac{n_2}{n_0}]\), ..., \([\frac{n_x}{n_0}]\) lies between 1 and 9(both included).
\(LCM(1,2,3,4,5,6,7,8,9) = 2^3*3^2*5*7 =2520 \)
Bunuel wrote:
If \(n_0\), \(n_1\), \(n_2\), ..., \(n_x\) are consecutive ascending positive integers from \(n_0\) to \(n_x\) such that \(n_x= 10n_0– 1\), what is the least common multiple of \([\frac{n_0}{n_0}]\), \([\frac{n_1}{n_0}]\), \([\frac{n_2}{n_0}]\), ..., \([\frac{n_x}{n_0}]\), where [k] is the greatest integer less than or equal to k ?
A. 9
B. 280
C. 2,520
D. 362,880
E. Cannot be determined
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions