Divisible 79464

The teacher wrote a number less than 50,000 on the board.
The first student said: This number is divisible by 2
The second student said: This number is divisible by 3
And so on, down to the last one who claimed it was divisible by 13. Two in a row lied.
What number did the teacher write, and which two lied?

Correct answer:

n =  25740

Step-by-step explanation:

4=22 5 ...  prime number 6=23 7 ...  prime number 8=23 9=32 10=25 11 ...  prime number 12=223 13 ...  prime number LCM(4,5,6,7,8,9,10,11,12,13)=2332571113=360360  a1=LCM(4,5,6,7,8,9,10,11,12,13)=360360 2 ...  prime number LCM(2,5,6,7,8,9,10,11,12,13)=2332571113=360360  a2=LCM(2,5,6,7,8,9,10,11,12,13)=360360 3 ...  prime number LCM(2,3,6,7,8,9,10,11,12,13)=2332571113=360360  a3=LCM(2,3,6,7,8,9,10,11,12,13)=360360 LCM(2,3,4,7,8,9,10,11,12,13)=2332571113=360360  a4=LCM(2,3,4,7,8,9,10,11,12,13)=360360 LCM(2,3,4,5,8,9,10,11,12,13)=233251113=51480  a5=LCM(2,3,4,5,8,9,10,11,12,13)=25740 LCM(2,3,4,5,6,9,10,11,12,13)=223251113=25740  a5=LCM(2,3,4,5,6,9,10,11,12,13)=25740 LCM(2,3,4,5,6,7,10,11,12,13)=223571113=60060  a6=LCM(2,3,4,5,6,7,10,11,12,13)=60060 LCM(2,3,4,5,6,7,8,11,12,13)=233571113=120120  a7=LCM(2,3,4,5,6,7,8,11,12,13)=120120 LCM(2,3,4,5,6,7,8,9,12,13)=23325713=32760  a8=LCM(2,3,4,5,6,7,8,9,12,13)=32760 LCM(2,3,4,5,6,7,8,9,10,13)=23325713=32760  a9=LCM(2,3,4,5,6,7,8,9,10,13)=32760 LCM(2,3,4,5,6,7,8,9,10,11)=23325711=27720  a10=LCM(2,3,4,5,6,7,8,9,10,11)=27720  n=a5=25740



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