Question

Find the number of positive integer <=3000 and divisible by 3 5 7

Answer 1

Answer:

hello friend your answer is here :

ans:1629

Step-by-step explanation:

#include<iostream>

using namespace std;

int main()

{

   int num=0,i;

   for(i=1;i<3001;i++)

   {

       if(i%3==0 || i%5==0 || i%7==0)

       {

           num++;

       }

   }

   cout<<num;

}

Answer 2

Answer:

There are 28 positive numbers ≤3000 that are divisible by 3,5,7

Step-by-step explanation:

The smallest number divisible by 3,5,7 = LCM of the numbers 3,5,7

Since 3,5,7 are prime numbers,

LCM of the numbers 3,5,7 = 3×5×7 = 105

The least positive number divisible by 3,5,7 is 105

The set of numbers divisible by 3,5,7, ........... = 105,210, 315,420,.......

To find the largest multiple of 3,5,7 less than or equal to  3000

The largest element multiple of 3,5,7 less than or equal to 3000 =  The largest multiple of 105 less than 3000

we have, 3000 = 28*105 + 60

Then, 3000 - 60 = 28*105

2940 = 28*105

∴ The largest multiple of 105 less than or equal to 3000 = 2940

Hence, the positive integers ≤ 3000 divisible by 3,5,7  =

105,210, 315,420,......., 2940

Since, 2940 is 28th multiple of 105, there are 28 elements in this set

Hence there are 28 positive numbers ≤3000 that are divisible by 3,5,7

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