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

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,

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: (c)

LCM = 2 × 2 × 3 × 3 × 7 × 8 = 2016

∴Required number = 2016 × 2 = 4032