Math, asked by Anonymous, 4 months ago

Find the least number of 7 digits that is exactly divisible by 16,18,24 and 30.

Answers

Answered by BrainlyUnnati
16

AnsWer :

1,000,080.

SolutioN :

Condition : The least number of 7 digits be 1000000.

Let the number be

  • N1 = 16.
  • N2 = 18.
  • N3 = 24.
  • N4 = 30.

Now,

2 | 16

2 | 8

2 | 4

2 | 2

| 1

_______________

2 | 18

3 | 9

3 | 3

| 1

_______________

2 | 24

2 | 12

2 | 6

3 | 3

| 1

_______________

3 | 30

2 | 10

5 | 5

| 1

LCM → 16 , 18 , 24 and 30

→ 2 * 2 * 2 * 2 , 2 * 3 * 3 , 2 * 2 * 2 * 3 , 3 * 2 * 5

→ 2⁴ * 3² * 5.

→ 720.

_______________

Now, Let

  • Dividend = The least number of 7 digits.
  • Divisior = 720.

720 ) 1000000 ( 1388

720

_________

2800

2166

__________

6400

5760

___________

6400

5760

__________

640

  • So, We can write as, The least number of 7 digits = 1000000.
  • Required number is 1000000 + ( Divisior - Remainder )

→ 1,000,000 + ( 720 - 640 )

→ 1,000,000 + ( 80 )

→ 1,000,080.

________________________________

VerificatioN :

  • N1 = 16.

Let check N1 is exactly divisible by 1,000,080

→ 1,000,080 / N1

→ 1,000,080 / 16

→ 62,505.

__________________

  • N2 = 18.

→ 1,000,080 / N2

→ → 1,000,080 / 18

→ 55,560.

__________________

  • N3 = 24.

→ 1,000,080 / N3

→ → 1,000,080 / 24

→ 41,670.

__________________

  • N4 = 30.

→ 1,000,080 / N4

→ → 1,000,080 / 30

→ 33,336.

Therefore, the value of 7 least digits number that is exactly divisible by 16,18,24 and 30 is 1,000,080.

Answered by bebrainlyindia74
5

Answer:

AnsWer :

1,000,080.

SolutioN :

Condition : The least number of 7 digits be 1000000.

Let the number be

N1 = 16.

N2 = 18.

N3 = 24.

N4 = 30.

Now,

2 | 16

2 | 8

2 | 4

2 | 2

| 1

_______________

2 | 18

3 | 9

3 | 3

| 1

_______________

2 | 24

2 | 12

2 | 6

3 | 3

| 1

_______________

3 | 30

2 | 10

5 | 5

| 1

LCM → 16 , 18 , 24 and 30

→ 2 * 2 * 2 * 2 , 2 * 3 * 3 , 2 * 2 * 2 * 3 , 3 * 2 * 5

→ 2⁴ * 3² * 5.

→ 720.

_______________

Now, Let

Dividend = The least number of 7 digits.

Divisior = 720.

720 ) 1000000 ( 1388

720

_________

2800

2166

__________

6400

5760

___________

6400

5760

__________

640

So, We can write as, The least number of 7 digits = 1000000.

Required number is 1000000 + ( Divisior - Remainder )

→ 1,000,000 + ( 720 - 640 )

→ 1,000,000 + ( 80 )

→ 1,000,080.

________________________________

VerificatioN :

N1 = 16.

Let check N1 is exactly divisible by 1,000,080

→ 1,000,080 / N1

→ 1,000,080 / 16

→ 62,505.

__________________

N2 = 18.

→ 1,000,080 / N2

→ → 1,000,080 / 18

→ 55,560.

__________________

N3 = 24.

→ 1,000,080 / N3

→ → 1,000,080 / 24

→ 41,670.

__________________

N4 = 30.

→ 1,000,080 / N4

→ → 1,000,080 / 30

→ 33,336.

Therefore, the value of 7 least digits number that is exactly divisible by 16,18,24 and 30 is 1,000,080.

Step-by-step explanation:

Similar questions