model 4 addition, subtraction, multiplication and division with lcm & hcf Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

Let the numbers be x, y and z which are prime to one another.

Now, xy = 551 yz = 1073

∴ y = HCF of 551 and 1073

y = 29

x = $551/29$ = 19

and z = $1073/29$ = 37

∴Sum = 19 + 29 + 37 = 85

Answer: (a)

Using Rule 1,

1st number × 2nd number = L.C.M. × H.C.F

LCM = 2 × 2 × 3 × 3 × 7= 252

The largest 4-digit number = 9999

∴ Required number = 9999 – 171 = 9828

Answer: (c)

HCF of two numbers = 27

Let the numbers be 27x and 27y

where x and y are prime to each other.

According to the question,

27x + 27y = 216

27 (x + y) = 216

x + y = $216/27$ = 8

Possible pairs of x and y = (1, 7) and (3, 5)

Numbers =(27, 189) and (81, 135)

Answer: (d)

210 = 2 × 3 × 5 × 7 = 5 × 6 × 7

∴ Required answer = 5 + 6 = 11

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: (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