A number theory problem by Dinesh Nath Goswami

Number Theory Level 2

Find the smallest positive integer that is perfectly divisible by all the integers from 1 to 10 inclusive.


The answer is 2520.

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Dinesh Nath Goswami by Dinesh Nath Goswami , 20, India

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3 solutions

Saran Balachandar
Oct 19, 2015

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Aditya Paul
Oct 22, 2015

Logically a number divisible by 7,8,9,10 have to be divisible by all numbers 1 to 6, so they are ignored. Now ws see 7 and 9 are prime so they can be simply multiplied. But for 8 and 10 we need to take LCM as simple product returns a larger answer. So LCM is 40. Now the answer is 40* 7* 9 =2520

1 Helpful 0 Interesting 0 Brilliant 0 Confused

7 is prime not 9

Courtney Rozsa - 5 years, 7 months ago

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he meant to say relatively prime to each other

John Rebo Santos - 5 years, 5 months ago

Yeah I'm sorry, I meant that 7 and 9 are relatively prime to each other as John has pointed out.

Aditya Paul - 5 years, 5 months ago

Just LCM of the numbers is the answer.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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