IIT JEE , AIEEE Forum - Mathematics , Algebra

arvind.b

there has to be some trick involved in these questions, otherwise i'd just write computer programs for them :).

Anyway, here's a solution for the division by 1 to 20

Let's first see why 2520 worked out for the 1 to 10 example

Begin by multiplying out all the primes from 1 to 10, so that is 2*3*5*7=210
So we've taken care of 2,3,5,6,7,10 by doing this.

To take care of 4 ... we need to multiply by 2 ..so now our number is 420

To take care of 8.. multiply by 2 again ... 840

Finally to take care of 9 .. multiply by 3 and end up with 2520

For 1 to 20 the same logic can be applied

first 2*3*5*7*11*13*17*19 = 9699690

numbers taken care of ... 1,2,3,5,6,7,10,11,13,14,15,17,19

for 4 .. multiply by 2 = 2*3*5*7*11*13*17*19*2

numbers taken care of ... 1,2,3,4,5,6,7,10,11,12,13,14,15,17,19,20

for 8 ..multiply by 2 = 2*3*5*7*11*13*17*19*2*2

numbers taken care of ... 1,2,3,4,5,6,7,8,10,11,12,13,14,15,17,19,20

for 9 .. multiply by 3 = 2*3*5*7*11*13*17*19*2*2*3

numbers taken care of ... 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20

only 16 is left, take care of that by multiplying by 2

2^4*3^2*5*7*11*13*17*19

232792560

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