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

Answer: (c)

Let the number be 29x and 29y respectively

where x and y are prime to each other.

∴ LCM of 29x and 29y = 29xy

Now, 29xy = 4147

∴ xy = $4147/29$ = 143

Thus xy = 11 × 13

∴ Numbers are 29 × 11

= 319 and 29 × 13 = 377

∴ Required sum

= 377 + 319 = 696

Answer: (b)

Let the numbers be 17x and 17y

where x and y are co-prime.

LCM of 17x and 17y = 17 xy

According to the question,

17xy = 714

⇒ xy = $714/17$ = 42 = 6 × 7

⇒ x = 6 and y = 7

or, x = 7 and y =6.

First number = 17x = 17 × 6 = 102

Second number = 17y =17 × 7 = 119

∴ Sum of the numbers = 102 + 119 = 221

Answer: (c)

Let the numbers be 2x and 2y

where x and y are prime to each other.

∴LCM = 2xy

⇒ 2xy = 84

⇒ xy = 42 = 6 × 7

∴ Numbers are 12 and 14.

Hence Sum = 12 + 14 = 26

Answer: (d)

Using Rule 1,

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

Let the numbers be x and (x + 2).

∴ Product of numbers = HCF × LCM

⇒ x (x + 2) = 24

⇒ $x^2$ + 2x – 24 = 0

⇒ $x^2$ + 6x – 4x – 24 = 0

⇒ x (x + 6) – 4 (x + 6) = 0

⇒ (x – 4) (x + 6) = 0

⇒ x = 4, as x ≠ 6 = 0

∴ Numbers are 4 and 6.

Answer: (b)

Let the number be x and y.

According to the question,

x + y = 45 ......... (i)

Again, x – y = $1/9$(x + y)

x – y = $1/9$×45

or x – y = 5 ..... (ii)

By (i) + (ii) we have,

x + y = 45

$\text"x – y = 5"/\text"2x"$ = 50

or, x = 25

y = 45 – 25 = 20.

Now, LCM of 25 and 20 = 100.