Find the number nearest to 24001 and between 24001 and 25000 divisible by 16, 24, 40

To find the required number we must find the l.c.m. of 16, 24 and 40.

16 = 2 × 2 × 2 × 2

24 = 2 × 2 × 2 × 3

40 = 2 × 2 × 2 × 5

l.c.m.(16, 24, 40) = 2 × 2 × 2 × 2 × 3 × 5 = 240

To find the number between 24001 and 25000,

Divide 24001 by 240

= 100. 004

So, the integer nearer to and greater than it is 101.

Hence, a number divisible by 240 and between 24001 and 25000 = 101 × 240 = 24240