Find the greatest 5 digit number that is exactly divisible by 22,25 and 30

Numbers 22,25 and 30

To find :

The greatest 5 digit number which is exactly divisible by 22,25 and 30

Solution :

If a number is divisible 22,25 and 30, then it must be a multiple for these numbers.

Let us find the smallest number which is divisible by 22,25 and 30. This is nothing but LCM of 22,25 and 30.

$2 \times 5 \times 3 \times 11 \times 5 = 1650$

So LCM is 1650.

The required number should be a multiple of 1650. It is also the smallest 5 digit number which is a multiple of 1650.

If we divide 10000 with 1650, we get a reminder of 100.

So 9900 is a multiple of 1650.

9900+ 1650 = 11550.

11550 is smallest 5 digit number which is multiple of 1650.

So, answer is 11550.