Question

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

Answer 1

31

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:

=
`(first number - last number )/(315) + 1`

=
`(9765 - 315)/(315)` + 1

= 30 + 1

= 31