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

Answer: (b)

HCF of two numbers = 4.

Hence, the numbers can be given by 4x and 4y

where x and y are co-prime.

Then, 4x + 4y = 36

4 (x + y) = 36

x + y = 9

Possible pairs satisfying this condition are : (1, 8), (4, 5), (2, 7)

Answer: (a)

Using Rule 1,

If the HCF = H,

then LCM = 44 H

44 H + H = 1125

→ 45 H = 1125

∴ H = $1125/45$ = 25

LCM = 44 × 25 = 1100

Now, First number × Second number = LCM × HCF

→ 25 × Second number = 1100 × 25

∴ Second number = ${1100 × 25}/25$ = 1100

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

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: (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