6 = 2 × 3

9 = 3²

15 = 3 × 5

LCM of 6 ,9 and 15 = 2 × 3² × 5 = 90

Perfect square number greater than 90 is 100

Required number = 100 – 90 = 10

Let the numbers be 5x and 4x

HCF of 5x and 4x = x = 4

Numbers are (5 × 4),(4 × 4) = 20, 16

20 = 5 × 4

16 = 4 × 4

LCM of 20 and 16 = 5 × 4 × 4 = 80

15 = 3 × 5

18 = 2 × 3²

25 = 5²

32 = 2⁵

LCM of 15, 18 , 25 and 32 =  2⁵ × 3² × 5² = 7200

Required number =  = 3600

"Hence, option A is the correct answer."

391 = 17 × 23

∴ HCF of 2040 and 391 is 17

Hence, option D is the correct answer.

HCF of two numbers = 3

∴ LCM of the numbers = 6 × 5 × 3 = 90

(30)⁴ = 2⁴ × 3⁴ × 5⁴

Divisors that are distinct natural numbers

= (4 + 1) × (4 + 1) × (4 + 1) = 5 × 5 × 5 = 125

According to question, milk in containers A, B and C are 637liters, 707 liters and 1523 liters respectively

Taken milk by ram from container A = 8 liters

Taken milk by ram from container B = 4 liters

Taken milk by ram from container C = average of A and B =  = 6 liters

Remaining milk in container A = 637 – 8 = 629 liters

Remaining milk in container B = 707 – 4 = 703 liters

Remaining milk in container C = 1523 – 6 = 1517 liters

For equal volume HCF of 629, 703 and 1517 = 37

Now, required bottle for container A = = 17

Required bottle for container B =  = 19

Required bottle for container C = = 41

Therefore, required total number of bottles = 17 + 19 + 41 = 77

Smallest number that is divisible by each of the numbers 6, 8 and 15 is LCM of 6, 8 and 15, i.e., 120.

Thus the number is of form 120k where k is a natural number.

Among the given options only 3600 is divisible by 120.

So, the required number is 3600.

Hence, the correct answer is option D.

Let the numbers be 2x and 3x.

Concept:

Multiplication of two numbers = Multiplication of their LCM and HCF

⇒(2x) × (3x) = 286 × 1716

⇒6x² = 286 × 1716

⇒x² =

⇒x² = 286 × 286

⇒x = 286

Therefore, the greater number is 286 × 3 = 858

Since absolute ratio of the numbers and HCF of the numbers are given, the numbers are 9 × 13 = 117 and 17 × 13 = 221.

Now, LCM of 117 and 221 = 117 × 17 = 1989

Alternate:

Since absolute ratio of the numbers and HCF of the numbers are given, the LCM of the numbers is 9 × 17 × 13 = 1989