Question

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

Answer 1

Answer:

procedure-find lcm

9999/lcm

9999-r

the answer is 9600

Answer 2

Answer:

9600 is the greatest number of 4 digits exactly divisible by 24, 60 and 96.

Given Data:

24, 60 and 96

Step 1:

First of all we will find the LCM of 24, 60 and 96.

24= $2 \times 2 \times 2 \times 3$

60=$2 \times 2 \times 3 \times 5=2^{3} \times 5$

96=$2 \times 2 \times 2 \times 2 \times 2 \times 3=2^{5} \times 3$

Step 2:

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

The number will be multiple of 480

Step 3:

Greatest 4 digit number is 9999, but it is not divisible by any of these numbers

Greatest number divisible by 480=9999-remainder $\left(\frac{9999}{480}\right)$

Step 4:

480 gives remainder 399

$\frac{9999}{480}$

Therefore number is 9999–399=9600.