The ratio of two numbers = 5 : 7

HCF = 3

∴ LCM = 5 × 3 × 7 = 105

Hence, option B is the correct answer.

10 = 2 × 5

15 = 3 × 5

24 = 2³ × 3

32 = 2⁵

LCM of 10, 15, 24 and 32 = 2⁵ × 3 × 5 = 480

Required number = 3 × 480 + 7 = 1440 + 7 = 1447 = x

Sum of digits of x = 1 + 4 + 4 + 7 = 16

2675 – 5 = 2670 = 2 × 3 × 5 × 89

2320 – 6 = 2314 = 2 × 13 × 89

Required number = HCF of 2670 and 2314 = 2 × 89 = 178

398 – 7 = 391 = 17 × 23

437 – 12 = 425 = 5² × 17

5425 – 2 = 5423 = 11 × 17 × 29

Required number = HCF of 391, 425 and 5423 = 17

For least number of square tiles, we will take HCF of given dimensions 12 m 95 cm and 3 m 85 cm.

HCF of 1295 and 385 = 35

Therefore, the tiles should be of dimension 35 cm × 35 cm.

Required least no. of tiles =  = 407

Let the greater number be 7x.

Then, smaller number = (7x) ×  = 4x

Now, we know that multiplication of HCF and LCM of two numbers is equal to multiplication of these numbers.

Therefore,

HCF × LCM = Multiplication of numbers

⇒ 8 × 224 = (4x) × (7x)

⇒ 28x² = 1792

⇒ x² = 1792/28

⇒ x² = 64

⇒ x =  = 8

Therefore, greater number = 7x = 7 × 8 = 56

Hence, option D is the correct answer.

The number will be difference of 33852 and 22965 or factor of it = 33852- 22965 = 10887

Factors of 10887 = 3×19×191

So, possible three digit numbers are 191 and 191×3.

Therefore, two numbers 191 and 573 are possible.

We will find common factor and common multiple of 14 and 18 respectively.

14 = 2 × 7 and 18 = 3 × 3 × 2

HCF = 2 and

LCM = 2 × 7 × 9 = 126

∴ HCF : LCM = 2 : 126 = 1 : 63

Highest common factor of 2³ × 3⁵ and 3³ × 5²

Here only 3³ is common.

Therefore, the Highest Common Factor of 2³ × 3⁵ and 3³ × 5² is 3³.

First number × second number = LCM × HCF

⇒ 77 × second number = 693 × 11

⇒ second number = 99

Hence, option B is the correct answer.