Question: 1 -

Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Their H.C.F. is:

10

20

40

30

Answer:

20

Solution:

Let the numbers be 2x, 3x and 4x
LCM of 2x, 3x and 4x = 12x
=> 12x = 240
=> x = 20
H.C.F of 2x, 3x and 4x is : x= 20

Question: 2 -

The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25,
 then the other is:

30

20

28

24

Answer:

30

Solution:

Product of two numbers = Product of their HCF and LCM.
Let one number = X
=> 25 × x =  5 × 150
=> x = 30
 

Question: 3 -

What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?

9600

9800

9200

9400

Answer:

9600

Solution:

Greatest number of four digits = 9999
LCM of 15, 25, 40 and 75 = 600
9999 ÷ 600 = 16, remainder = 399
Hence, greatest number of four digits which is divisible by 15, 25, 40 and 75
= 9999 - 399 = 9600

Question: 4 -

Two numbers are in the ratio 2 : 3. If their L.C.M. is 48. what is sum of the numbers?

42

40

28

64

Answer:

40

Solution:

Let the numbers be 2x and 3x
LCM of 2x and 3x = 6x (? LCM of 2 and 3 is 6. Hence LCM
of 2x and 3x is 6x)
Given that LCM of 2x and 3x is 48
=> 6x = 48
=> x = 48/6 = 8
Sum of the numbers = 2x + 3x = 5x = 5 × 8 = 40

Question: 5 -

 What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?

1683

3363

2007

1108

Answer:

1683

Solution:

LCM of 5, 6, 7 and 8 = 840
Hence the number can be written in the form (840k + 3) which is divisible by 9.
If k = 1, number = (840 × 1) + 3 = 843 which is not divisible by 9.
If k = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9.
Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.