A number theory problem by Sumon Jose

Number Theory Level 2

Which is the smallest positive integer that yields zero remainder when divided by 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10?


The answer is 2520.

Sumon Jose by Sumon Jose , 35, India

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7 solutions

Kishore Battula
Feb 13, 2014

LCM(1,2,3,4,5,6,7,8,9,10)

8 Helpful 0 Interesting 0 Brilliant 0 Confused

It should be 0 0 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Sharky Kesa - 7 years, 3 months ago

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Smallest positive integers doesn't include 0.

Kevin Mo - 7 years, 3 months ago

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It didn't say positive before.

Sharky Kesa - 7 years, 3 months ago

0 isn't positive

Bryan Sangtania - 7 years, 1 month ago

2520

Mallikarjuna Ragulakolla - 7 years, 2 months ago

Solution:

To find a positive integer take L.C.M of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Now, 6 is a multiple of 2 & 3. 8 is a multiple of 4. 10 is a multiple of 5.

So we can take LCM of 6 7 8 9 10.

Again 8 is a multiple of 2 and 9 is multiple of 3. So we can exclude 6 (3*2).

So now to take LCM of 7,8,9,10. Which is 2520.

Nishipalsinh Rana - 7 years ago

it should be 1680!!!!

Varsha Patra - 7 years, 3 months ago

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why varsha its 2520 forgot LCM :p...... prove how???1680/9=18.66,you dont call it divisible!!!

Ephraim Raj - 7 years, 3 months ago

1680 is not divisible by 9

Sufinsha Musthafa - 7 years, 2 months ago

it is not divisible by 9

Punith Bajaj - 7 years, 2 months ago

0 it should be

Kushal Agarwal - 7 years, 2 months ago

Very Good!

Mahiuddin Rasel - 7 years, 1 month ago

forgot lowest common multiple how to perfrom already lol

Zack Yeung - 7 years, 1 month ago

what about 63 ? it gives zero remainde.

Danish Ilyas - 7 years, 3 months ago

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63/10=6.3

Didarul Alam - 7 years, 3 months ago
Shamima Shimu
Mar 31, 2014

9 * 8 * 7 * 5 = 2520

2 Helpful 0 Interesting 0 Brilliant 0 Confused
M S Rumon
Mar 7, 2014

I've solved it using a simple c code. Here it is:

include<stdio.h>

int main() { int i,cou; for(i=1;;) { if(i%1==0&&i%2==0&&i%3==0&&i%4==0&&i%5==0&&i%6==0&&i%7==0&&i%8==0&&i%9==0&&i%10==0) { cou=i; break; } else i++; } printf("%d",cou); }

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Akshal Sarodia
Apr 22, 2014

take LCM of 1,2,3,4,5,6,7,8,9,10 which is 2520

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Hassan Rajput
Apr 22, 2014

LCM of numbers 1 2 3 4 5 6 7 8 9 10 which is equal to 2 2 2 3 3 5 7=2520

0 Helpful 0 Interesting 0 Brilliant 0 Confused
S W
Apr 18, 2014

LCM of 1,2,3,4,5,6,7,8,9,10

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Nilangini Gupta
Apr 17, 2014

LCM of numbers 1 to 10

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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