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

Answer: (d)

Using Rule 1,

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

Let the H.C.F. be H.

L.C.M. = 20H

Then, H + 20H = 2520

⇒ 21 H = 2520

⇒ H = $2520/21$ = 120

∴ L.C.M. = 20H = 20×120= 2400

As, First number × Second number = L.C.M. × H.C.F.

⇒ 480 × Second number = 2400 × 120

⇒ Second number = ${2400 × 120}/480$ = 600

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: (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: (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