The difference between the divisor and the corresponding remainder is same in each case
ie. 18 – 5 = 13, 27 – 14 = 13, 36 – 23 = 13
∴ Required number = (LCM of 18, 27, and 36 ) – 13
LCM of 18, 27, and 36 = 108

Correct Option: A

The difference between the divisor and the corresponding remainder is same in each case
ie. 18 – 5 = 13, 27 – 14 = 13, 36 – 23 = 13
∴ Required number = (LCM of 18, 27, and 36 ) – 13
LCM of 18, 27, and 36 = 108
Hence , Required number = 108 – 13 = 95

LCM of 9, 10 and 15 = 90
⇒ The multiple of 90 are also divisible by 9, 10 or 15.
∴ 21 × 90 = 1890 will be divisible by them.
∴ Now, 1897 will be the number that will give remainder 7.
∴ Required number = 1936 – 1897

Correct Option: C

LCM of 9, 10 and 15 = 90
⇒ The multiple of 90 are also divisible by 9, 10 or 15.
∴ 21 × 90 = 1890 will be divisible by them.
∴ Now, 1897 will be the number that will give remainder 7.
∴ Required number = 1936 – 1897 = 39

LCM of 5, 10, 12, 15

∴ LCM = 2 × 3 × 5 × 2 = 60
∴ Number = 60k + 2
Now, the required number should be divisible by 7.
Now, 60k + 2 = 7 × 8k + 4k + 2
If we put k = 3 , (4k + 2) is equal to 14 which is exactly divisible by 7.

Correct Option: B

LCM of 5, 10, 12, 15

∴ LCM = 2 × 3 × 5 × 2 = 60
∴ Number = 60k + 2
Now, the required number should be divisible by 7.
Now, 60k + 2 = 7 × 8k + 4k + 2
If we put k = 3 , (4k + 2) is equal to 14 which is exactly divisible by 7.
∴ Required number = 60 × 3 + 2 = 182

We have , The LCM of 12, 18, 21, 30

∴ LCM = 2 × 3 × 2 × 3 × 7 × 5 = 1260

Correct Option: C

We have , The LCM of 12, 18, 21, 30

∴ LCM = 2 × 3 × 2 × 3 × 7 × 5 = 1260

LCM of 6, 9, 15 and 18

∴ LCM = 2 × 3 × 3 × 5 = 90
∴ Required number = 90k + 4, which must be a multiple of 7 for some value of k.
For k = 4,

Correct Option: D

LCM of 6, 9, 15 and 18

∴ LCM = 2 × 3 × 3 × 5 = 90
∴ Required number = 90k + 4, which must be a multiple of 7 for some value of k.
For k = 4,
Required Number = 90 × 4 + 4 = 364, which is exactly divisible by 7.