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 solutionss.

Problems in Mathematics of KöMaL, October 2014