Question

Find the greatest number of five digits which
becomes exactly divisible by 10, 12, 15 and 18
when 3769 is added to it.​

Answer 1

Answer:

99900

Step-by-step explanation:

the LCM of the 10 ,12,15 and 18 is 180

Answer 2

Given:

The number should be divisible by 10, 12, 15 and 18

To find:

The greatest number of 5 digits that is divisible by given numbers

Solution:

The greatest number of 5 digits that is divisible by 10, 12, 15 and 18 when 3769 is added to it is 96,131.

We can find the number by following the given steps-

We know that for a number to be divisible by 10, 12, 15, 18, it has to be divisible by the LCM of 10, 12, 15, and 18.

The LCM of 10, 12, 15, 18=180

Now, we will find the greatest 5 digit number that is divisible by 180.

Also, the greatest 5 digits number is 99,999.

On dividing 99,999 by 180, we get

=99,999/180=99

The remainder is 99.

So, the greatest 5 digit number that is divisble by 180=99,999-99

=99,900

Now, the greatest 5 digit number before 3769 was added to it=99,900-3769

=96,131

Therefore, the greatest number of 5 digits that is divisible by 10, 12, 15 and 18 when 3769 is added to it is 96,131.