Question

Find the greatest number of 4 digits exactly divisible by 24, 60 and 96.

Answer 1

Answer:

Thus 9600 is greatest 4-digit number,which is completely divisible by 24,60 and 96.

Solution:

To find the greatest number of 4 digits exactly divisible by 24, 60 and 96.

First find the LCM of 24,60 and 96

$24 = 2 \times 2 \times 2 \times 3 \\ 60 = 2 \times 2 \times 3 \times 5 \\ 96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \\ \\ LCM(24, \: 60, \: 96) = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 5 \\ \\ = {2}^{5} \times 3 \times 5 \\ \\ = 32 \times 15 \\ \\ = 480$

480 is that number which completely divisible by 24,60,96

but what we need is a number which is of 4 digit,so find the multiple of 480

$multiple \: of \: 480 = 480 \times 2 \:... \: 480 \times 20 \\ \\ = 9600$

Thus 9600 is greatest 4-digit number,which is completely divisible by 24,60,96.

Hope it helps you.