Question

find the least number of 7 digits that is exactly divisible by 16,18,24 and 30.
please answer it is very urgent.
spam or incorrect answers would be reported.​

Answer 1

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.

Answer 2

$\mathfrak{\huge{\underline{\underline{\red{Question\:?}}}}}$

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

$\mathfrak{\huge{\underline{\underline{\green{Answer:-}}}}}$

✒ The least number of 7 digits that is exactly divisible by 16,18,24 and 30 is 1014480 .

$\mathcal{\huge{\underline{\underline{\pink{SoLuTiOn:-}}}}}$

According to the question,

2 | 16

2 | 8

2 | 4

2 | 2

1. | 1

____

2 | 18

3 | 9

3 | 3

1. | 1

_____

2 | 24

2 | 12

2 | 6

3 | 3

1. | 1

_____

3 | 30

2 | 10

5 | 5

1. | 1

_____

⭐ 16 = 2 × 2 × 2 × 2

⭐ 18 = 2 × 3 × 3

⭐ 24 = 2 × 2 × 2 × 3

⭐ 30 = 2 × 3 × 5

LCM(16,18,24,30) = 2 × 2 × 2 × 2 × 3 × 3 × 5

=> 720

Taking dividend as the least number of 7 digits , (1000000)

▶ Deviding , 1000000 by 720

➡ 1000000 ÷ 720 ≈ 1409 (approx.)

▶ The lowest five digit number is Dividing 1000000 by 720 gives you 13888.8888. Round that up to 14, and then multiply by 720 to get your answer.

➡ 1409×720 = 1014480

✅ Verification :-

1014480 ÷ 16 = 63405

1014480 ÷ 18 = 56350

1014480 ÷ 24 = 42270

1014480 ÷ 30 = 33816

✏ It clearly shows 1014480 is exactly divisible by 16,18,24 and 30.

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