Question

1. How many numbers less than 10,000 are there which are divisibleby 21, 35 and 63?​

Answer 1

Answer:

31

Step-by-step explanation:

To solve this problem, we must find the lowest common multiple of 21, 35 and 63

   Find the prime factors of the number;

 Prime factors of 21  = 3 x 7

                            35 = 3 x 5

                            63 = 3 x 3 x 7

  The lcm = 3 x 3 x 5 x 7 = 315

The numbers between  1 and 10, 000 divided by these three numbers;

   First number  = 315

    Last number  = 9765

Now the total number:

      = $\frac{first number - last number }{315} + 1$

      = $\frac{9765 - 315}{315}$ + 1

     = 30 + 1

     = 31