Question

Find the greatest number of five digits exactly divisible by by9, 12,15,18 and 24​

Answer 1

Given :

•The greatest number of five digits exactly divisible by 9,12,15,18 and 24 .

To Find :

•The greatest number of five digits exactly divisible by 9,12,15,18 and 24=?

Solution :

•The greatest 5 digit number is 99999 .

Now,Find the LCM of 9,12,15,18 and 24 .

2 |9 12 15 18 24

2 |9 6 15 9 12

2 | 9 3 15 9 6

3 | 9 3 15 9 3

3 | 3 1 5 3 1

5 | 1 1 5 1 1

| 1 1 1 1 1

LCM(9,12,15,18,24)

$\implies \sf \: 2 \times 2 \times 2 \times 3 \times 3 \times 5$

LCM(9,12,15,18,24)=360

•Divide 99999 by 360 so that we get the remainder,

$\implies \sf \: 99999 = 277 \times 360 + 279$

Remainder is 279.

•Now subtract the remainder from 99999.

$\implies \sf \: 99999 - 279 = 99720$

Therefore, the required number is 99720 which is exactly divisible by 9,12,15,18 and 24 .

Answer 2

Step-by-step explanation:

Given :

•The greatest number of five digits exactly divisible by 9,12,15,18 and 24 .

To Find :

•The greatest number of five digits exactly divisible by 9,12,15,18 and 24=?

Solution :

•The greatest 5 digit number is 99999 .

Now,Find the LCM of 9,12,15,18 and 24 .

2 |9 12 15 18 24

2 |9 6 15 9 12

2 | 9 3 15 9 6

3 | 9 3 15 9 3

3 | 3 1 5 3 1

5 | 1 1 5 1 1

| 1 1 1 1 1

LCM(9,12,15,18,24)

$\implies \sf \: 2 \times 2 \times 2 \times 3 \times 3 \times 5$

LCM(9,12,15,18,24)=360

•Divide 99999 by 360 so that we get the remainder,

$\implies \sf \: 99999 = 277 \times 360 + 279$

Remainder is 279.

•Now subtract the remainder from 99999.

$\implies \sf \: 99999 - 279 = 99720$

Therefore, the required number is 99720 which is exactly divisible by 9,12,15,18 and 24 .