Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4653. (October 2014)

B. 4653. How many ordered triples of positive integers $\displaystyle a$, $\displaystyle b$, $\displaystyle c$ are there for which $\displaystyle [a,b,c]=10!$ and $\displaystyle (a,b,c)=1$? ($\displaystyle (a,b,c)$ denotes the greatest common divisor, and $\displaystyle [a,b,c]$ denotes the least common multiple.)

(4 pont)

Deadline expired on November 10, 2014.

### Statistics:

 208 students sent a solution. 4 points: 81 students. 3 points: 19 students. 2 points: 37 students. 1 point: 46 students. 0 point: 20 students. Unfair, not evaluated: 5 solutions.

Problems in Mathematics of KöMaL, October 2014