As we know that when a number is divided by a, b or c leaving remainders p, q and r respectively such that the difference between divisor and remainder in each case is same i.e., (a – p) = (b – q) = (c – r) = t (say) then that (least) number must be in the form of (k – t), where k is LCM of a , b and c .
The smallest number divisible by 12 or 10 or 8
= LCM of 12, 10 and 8 = 120
remainder = 6

Correct Option: C

As we know that when a number is divided by a, b or c leaving remainders p, q and r respectively such that the difference between divisor and remainder in each case is same i.e., (a – p) = (b – q) = (c – r) = t (say) then that (least) number must be in the form of (k – t), where k is LCM of a , b and c .
The smallest number divisible by 12 or 10 or 8
= LCM of 12, 10 and 8 = 120
remainder = 6
∴ Required number = 120 + 6 = 126

As we know that when a number is divided by a, b or c leaving remainders p, q and r respectively such that the difference between divisor and remainder in each case is same i.e., (a – p) = (b – q) = (c – r) = t (say) then that (least) number must be in the form of (k – t), where k is LCM of a , b and c .
LCM of 15, 20 and 35 ( k ) = 420
Here , remainder = 8

Correct Option: A

As we know that when a number is divided by a, b or c leaving remainders p, q and r respectively such that the difference between divisor and remainder in each case is same i.e., (a – p) = (b – q) = (c – r) = t (say) then that (least) number must be in the form of (k – t), where k is LCM of a , b and c .
LCM of 15, 20 and 35 ( k ) = 420
Here , remainder = 8
∴ Required least number = 420 + 8 = 428

As we know that when a number is divided by a, b or c leaving remainders p, q and r respectively such that the difference between divisor and remainder in each case is same i.e., (a – p) = (b – q) = (c – r) = t (say) then that (least) number must be in the form of (k – t), where k is LCM of a , b and c .
Here, t = 12 – 2 = 10; 16 – 6 = 10; 24 – 14 = 10
Now, LCM of 12, 16 and 24 = 48
∴ The greatest 4–digit number exactly divisible by 48 = 9984

Correct Option: A

As we know that when a number is divided by a, b or c leaving remainders p, q and r respectively such that the difference between divisor and remainder in each case is same i.e., (a – p) = (b – q) = (c – r) = t (say) then that (least) number must be in the form of (k – t), where k is LCM of a , b and c .
Here, t = 12 – 2 = 10; 16 – 6 = 10; 24 – 14 = 10
Now, LCM of 12, 16 and 24 = 48
∴ The greatest 4–digit number exactly divisible by 48 = 9984
∴ Required number = 9984 – 10 = 9974

The LCM of 5, 6, 7 and 8 = 840
∴ Required number = 840k + 3 , which is exactly divisible by 9 for some value of k.
Now, 840k + 3 = 93 × 9k + (3k + 3)
When k = 2 , 3k + 3 = 9, which is divisible by 9.
∴ Required number = 840k + 3

Correct Option: B

The LCM of 5, 6, 7 and 8 = 840
∴ Required number = 840k + 3 , which is exactly divisible by 9 for some value of k.
Now, 840k + 3 = 93 × 9k + (3k + 3)
When k = 2 , 3k + 3 = 9, which is divisible by 9.
∴ Required number = 840k + 3 = 840 × 2 + 3 = 1683

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