Question

Find the greatest number of four digits which is divisible by 15, 20 and 25. with solution

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Answer 1

The Largest 4 digit number which is divisible by 15, 20 and 25 is 9900.

Step-by-step explanation:

I believe your Question was,

"Find the largest 4 digit number which is divisible by 15, 20 and 25"

We know that,

The Largest 4 digit number is 9999, which means it is a number that is below 9999 or it can be 9999 itself.

LCM of 15, 20 and 25 will give the lowest common multiple

15 = 3 × 5

20 = 2 × 2 × 5 = 2² × 5

25 = 5 × 5 = 5²

LCM = 2² × 3 × 5² = 300

The L.C.M. of given numbers is 300. It means that, the largest 4 digit number which is divisible by 15 20 and 25 must be also divisible by 300.

so, 9999 ÷ 300

Quotient = 33 and Remainder = 99

Now, we know that,

When a Dividend is divided by a Divisor and a Remainder is formed then, to get a perfect Quotient (where the remaider is 0) we must Subtract the Dividend and Remainder and divide it again to get a perfect Quotient

it means

Ex:- 16 ÷ 5

Quotient = 3 and Remainder = 1

Now, to get a perfect Quotient we must have remainder 0

So,

16 - 1 = 15

Now, 15 ÷ 5 = 3 and Remaider = 0

Similarly,

To get a perfect Quotient,

we should subtract 9999 and 99

9999 - 99 = 9900

Therefore the Largest 4 digit number which is divisible by 15, 20 and 25 is 9900.

Hope it helped and you understood it........All the best