Answer: Option B

Explanation:
HCF of two numbers = 29
Let the numbers = 29x, 29y
x and y are prime to each other
According to the question,
29x + 29y = 232,  29(x+y) = 232, x + y = 8,
Possible pairs of x and y = (1,7) and (3,5)
numbers are = (29, 203) and (87,145)  

Answer: Option C

Explanation:
Let the numbers be x and y
According to the problem
X + y = 63
x - y  = 1/8 ( x+y)
x-y = 1/8 * 63,  x-y = 9
2x = 72, x= 36 and y = 27
L.C.M of 36 and 27 is  351

Answer: Option D

Explanation:
L.C.M =   L.C.M of numerator/ H.CF of denominator
L.C.M = L.C.M of 2,5,4 / H.C.F of 7, 14, 21,
L.C.M =   20/7,
L.C.M = 2 6/7

Answer: Option B

Explanation:
H.CF = H.C.F of numarator/L.C.M of denominator
H.C.F = H.C.F of 1, 3, 7 / L.C.M of 3, 5, 12
H.C.F = 1/60 

Answer: Option C

Explanation:
The other number is = 36 * 1600/160  = 360  

Answer: Option B

Explanation:
The difference between any divisor and the corresponding remainder is 14,
L.C.M of 26,36,46  -14
= 10764-14
= 10750

Answer: Option B

Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 96
=> 12x = 96
=> x = 96/12 = 8
Sum of the numbers 
= 3x + 4x 
= 7x
= 7 x 8 = 56

Answer: Option B

Explanation:
Let the number be 2x, 3x and 4x 
LCM of 2x, 3x and 4x = 12x 
12x = 240 
=> x = 240/12 = 20
HCF of 2x, 3x and 4x = x = 20

Answer: Option C

Explanation:

LCM = 2 × 3 × 2 × 1 × 3 × 10 = 360

Answer: Option B

Explanation:
LCM of 5, 6, 7 and 8 = 840
Hence the number can be written in the form (840k + 3) which is divisible by 9.
If k = 1, number = (840 × 1) + 3 = 843 which is not divisible by 9.
If k = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9.
Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.