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 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 numbers be x H and yH

where H is the HCF and yH > x H.

LCM = xy H

xyH = 2yH

→ x = 2

Again, x H – H = 4

→ 2H – H = 4 ⇒ H = 4

∴ Smaller number = x H = 8

Answer: (a)

LCM = 2 × 2 × 3 × 4 × 3 × 7 = 1008

Multiple of 1008 = 2016

∴ Required number = 2016 – 2000 = 16 = x

∴ Sum of digits of x = 1 + 6 = 7

Answer: (d)

LCM of 8, 12 and 16 = 48

∴ Required number

= 48a + 3 which is divisible by 7.

x = 48a + 3 = (7 × 6a) + (6a + 3) which is divisible by 7.

i.e. 6a + 3 is divisible by 7.

When a = 3, 6a + 3 = 18 + 3 = 21

which is divisible by 7.

∴ x = 48 × 3 + 3 = 144 + 3 = 147