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

Answer: (d)

210 = 2 × 3 × 5 × 7 = 5 × 6 × 7

∴ Required answer = 5 + 6 = 11

Answer: (b)

LCM of 5, 6, 7 and 8 = 840

∴ LCM = 2 × 5 × 3 × 7 × 4 = 840

Required number = 840x + 3

which is divisible by 9 for a certain least value of x.

Now, 840x + 3 = 93x × 9 + 3x + 3

3x + 3, is divisible by 9 for x = 2

Required number = 840 × 2 + 3

= 1680 + 3 = 1683

∴ Sum of digits = 1 + 6 + 8 + 3 = 18

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,

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: (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: (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