Question

2. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. The sum of the
numbers is:
a) 28 b) 32 c) 40 d) 64
3. The sum of two numbers is 192 & their HCF is 24. The number of pairs of numbers
satisfying the above condition isa)
6 b) 5 c) 4 d) 2
4. How many numbers between 200 & 600 are divisible by 4, 5 & 6?
a) 5 b) 6 c) 7 d) 8
5. The H.C.F. of two numbers is 12 and their difference is 12. The numbers are :
a) 66, 78 b) 70, 82 c) 94, 106 d) 84, 96
6. What is the smallest number which when increased by 3, is fully divisible by 21, 25, 27
& 35.
a) 4735 b) 4635 c) 4725 d) 4722
7. The GCM of 24 & 36 isa)
12 b) 144 c) 24 d) 72

Answer 1

$\underline{\boxed{Question(1)}}$

The L.C.M. of two numbers is 48. The numbers are in the ratio 2:3 . The sum of the numbers is :

(a) 28  (b) 32 (c)40 (d) 64

$\underline{\boxed{Solution(1)}}$

Let, numbers are

2x and 3x ,

then

2 x = 2 * x

3 x = 3 * x

LCM ( 2x , 3x ) = 2 * 3 * x = 6 x

48 = 6 x

x = 8

so, sum of numbers= 2x + 3x = 2(8)+3(8) = 40

$\underline{\boxed{Question(2)}}$

The sum of  two numbers is 192 and their H.C.F is 24. The number of pairs of numbers satisfying the above condition is:

(a) 6 (b)5  (c)4 (d) 2

$\underline{\boxed{Solution(2)}}$

the H.C.F of numbers is 24

so, let numbers are

24 x   and  24 y

then,

24 x + 24 y = 192

24 ( x + y ) = 192

x+ y = 192 / 24

x + y = 8

so, numbers could be

( 1, 7 ),(2,6),(3,5),(4,4)

There are 4 such pairs.

$\underline{\boxed{Question(3)}}$

How many numbers between 200 and 600 are divisible by 4 , 5 and 6?

(a) 5 (b) 6 (c)7 (d)8

$\underline{\boxed{Solution(3)}}$

Let us find the LCM of 4 , 5 , 6

LCM(4,5,6) = 60

so, the numbers between 200 and 600 which are divisible by 60 will be divisible by 4 , 5 , 6 all

numbers divisible by 60 will be

240 , 300 , 360 , 420 , 480 , 540

so, there are 6 numbers between 200 and 600 divisible by 4 , 5 and 6 .

$\underline{\boxed{Question(4)}}$

The H.C.F of two numbers is 12 and their difference is 12 . the numbers are

(a) 66 , 78  (b)70 ,82  (c) 94, 106 (d) 84 , 96

$\underline{\boxed{Solution(4)}}$

H.C.F of two numbers is 12

it means both numbers should be divisible by 12 and their difference should be 12

here,

in the given alternatives

the difference in all is 12

but only in (4) alternative both numbers are divisible by 12.

$\underline{\boxed{Question(5)}}$

What is the smallest number which when increased by 3 , is fully divisible by 21 , 25 , 27 and 35

(a) 4735  (b) 4635  (c) 4725  (d) 4722

$\underline{\boxed{Solution(5)}}$

finding the LCM of 21, 25 , 27 , 35

we will get,

LCM (21,25,27,35) = 4725

subtracting 3 from their LCM we will get,

4725 - 3 = 4722

hence , our answer is 4722.

$\underline{\boxed{Question(6)}}$

The GCM of 24 and 36 is

(a) 12  (b)144 (c) 24 (d) 72

$\underline{\boxed{Solution(6)}}$

GCM = greatest common measure

also known as HCF commonly

so, HCF (24 , 36) = 12 .

Answer 2

$\large\red{\sf\:Answer}$

2. a) 28

3. a) 6

4. d) 8

5. d) 84, 96

6. c) 4725

$\large\pink{\sf\:Explanation}$

2. The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. The sum of the

numbers is

a) 28

3. The sum of two numbers is 192 & their HCF is 24. The number of pairs of numbers

satisfying the above condition is

a) 6

4. How many numbers between 200 & 600 are divisible by 4, 5 & 6?

d) 8

5. The H.C.F. of two numbers is 12 and their difference is 12. The numbers are :

d) 84, 96

6. What is the smallest number which when increased by 3, is fully divisible by 21, 25, 27& 35.

c) 4725