The greatest number of 4 digits = 9999
Now, we divide 9999 by 789

Thus, when 9999 – 531= 9468 is divided by 789, no remainder is left.
The required greatest number of
4 digits = 9468 + 5 = 9473
The least number of 5 digits
= 10000

Remainder = 532
∴  The least number of 5 digits exactly divisible by 789
= 10000 + (789 – 532)
= 10000 + 257 = 10257
∴  The required number
= 10257 + 5 = 10262
Remark : If 532 is subtracted from 10000 the number obtained 9468 is exactly divisible by 789 but in that case, the number will not be of 5 digits but of 4 digits.

Correct Option: A

The greatest number of 4 digits = 9999
Now, we divide 9999 by 789

Thus, when 9999 – 531= 9468 is divided by 789, no remainder is left.
The required greatest number of
4 digits = 9468 + 5 = 9473
The least number of 5 digits
= 10000

Remainder = 532
∴  The least number of 5 digits exactly divisible by 789
= 10000 + (789 – 532)
= 10000 + 257 = 10257
∴  The required number
= 10257 + 5 = 10262
Remark : If 532 is subtracted from 10000 the number obtained 9468 is exactly divisible by 789 but in that case, the number will not be of 5 digits but of 4 digits.

As we know, the first four prime numbers are 2, 3, 5, 7
Their product = 2 × 3 × 5 × 7 = 210
Now, we divide 12199 by 210

Here, D – R = 210 – 19 = 191
So, (D – R) > R.
Hence, the required number
= 12199 – R = 12199 – 19
= 12180

Correct Option: D

As we know, the first four prime numbers are 2, 3, 5, 7
Their product = 2 × 3 × 5 × 7 = 210
Now, we divide 12199 by 210

Here, D – R = 210 – 19 = 191
So, (D – R) > R.
Hence, the required number
= 12199 – R = 12199 – 19
= 12180

We divide 77685 by 720

Here, D – R = 720 – 645 = 75 < R.
∴  The required number
= 77685 + 75 = 77760

Correct Option: C

We divide 77685 by 720

Here, D – R = 720 – 645 = 75 < R.
∴  The required number
= 77685 + 75 = 77760

We divide 56586 by 552

∴  R = 282
D = 552
∴  D – R = 552 – 282 = 270
Here, (D – R) < R
So, we get the required number
by adding (D – R) to the dividend.
Therefore, the number nearest to 56586 that is exactly divisible by 552 is
56586 + 270 = 56856

Correct Option: B

We divide 56586 by 552

∴  R = 282
D = 552
∴  D – R = 552 – 282 = 270
Here, (D – R) < R
So, we get the required number
by adding (D – R) to the dividend.
Therefore, the number nearest to 56586 that is exactly divisible by 552 is
56586 + 270 = 56856

The least number of five digits = 10000
Now, we divide 10000 by 666

Here, we have 10 as remainder.
Therefore, the least number to be added to the least number of 5 digits, i.e., 10000 to get the least number of 5 digits which is exactly divisible by 666 is 666– 10 or 656.
Hence, the required number
= 10000 + 656 = 10656.

Correct Option: A

The least number of five digits = 10000
Now, we divide 10000 by 666

Here, we have 10 as remainder.
Therefore, the least number to be added to the least number of 5 digits, i.e., 10000 to get the least number of 5 digits which is exactly divisible by 666 is 666– 10 or 656.
Hence, the required number
= 10000 + 656 = 10656.