model 4 addition, subtraction, multiplication and division with lcm & hcf Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (d)

Firstly, we find the LCM of 30, 36 and 80.

LCM = 2 × 2 × 3 × 5 × 3 × 4 = 720

Required number = Multiple of 720 = 720 × 5 = 3600;

because 3000 < 3600 < 4000

Answer: (b)

Let the numbers be 3x and 3y.

∴ 3x + 3y = 36

⇒ x + y = 12 ... (i)

and 3xy = 105 ... (ii)

Dividing equation (i) by (ii), we have

$\text"x"/ \text"3xy" + \text"y"/ \text"3xy" = 12/105$

⇒ $1/\text"3y" + 1/\text"3x" = 4/35$

Answer: (a)

Using Rule 1,

Let the HCF of numbers = H

Their LCM = 12H

According to the question,

12H +H = 403

⇒ 13H = 403

⇒ H = $403/13$ =31

⇒ LCM = 12 × 31

Now, First number × second number

= HCF × LCM

= 93 × Second Number

= 31 × 31 × 12

Second number = ${31 × 31 × 12}/93$ = 124

Answer: (a)

Using Rule 1,

Suppose 1st number is x then, 2nd number = 100 – x

∴ LCM × HCF = 1st number × 2nd number

→ 495 × 5 = x × (100 – x)

→ 495 × 5 = 100x – $x^2$

→ $x^2$ – 55x – 45x – 2475 = 0

→ (x – 45) (x – 55) = 0

→ x = 45 or x = 55

Then, difference = 55 – 45 = 10

Answer: (d)

210 = 2 × 3 × 5 × 7 = 5 × 6 × 7

∴ Required answer = 5 + 6 = 11