16
Q:

LCD of 12 and 18

A) 36 B) 42
C) 12 D) 6

Answer:   A) 36



Explanation:

  LCD is nothing but Lowest or Least Common Denominator

 

Here LCD of 12 and 18 means LCD of two fractions with denominators 12 and 18 respectively.

 

Therefore, LCM of 12 & 18 = 6 x 3 x 2 = 36 

 

      •  How to calculate LCD ::


The lowest common denominator or least common denominator (LCD) is the least common multiple (LCM) of the denominators of a set of fractions.

Q:

Three different containers contain 1365 litres, 1560 litres and 1755 litres of mixtures of milk and water respectively. What biggest measure that can measure all the different quantities exactly ?

A) 37 lit B) 97 lit
C) 129 lit D) 195 lit
 
Answer & Explanation Answer: D) 195 lit

Explanation:

From the given data,

containers contain mixtures of milk and water as 1365 lit, 1560 lit and 1755 lit.

 

Biggest measure that can measure all these different quantities exactly can be given by

HCF of (1365, 1560, 1755) 

That can be found as 

 

HCF of 1365, 1755 = 195

Now, HCF of 195 and 1560 = 195

 

Hence, biggest measure that can measure all the given different quantities exactly is 195 lit.

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1 122
Q:

What is a Common Multiple?

Answer

If the Multiples for two or more numbers which are Common, then those Multiples are said to be Common Multiples. 


 


For Example :


Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,...


Multiples of 5 are 5, 10, 15, 20, 25, 30,...


Here common multiples of 3 & 5 upto 30 are 15, 30.

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19 1147
Q:

54, 60  LCM is

A) 600 B) 540
C) 60 D) 54
 
Answer & Explanation Answer: B) 540

Explanation:

Here the LCM of 54, 60 is

 

=> 2 x 3 x 3 x 3 x 10

= 6 x 9 x 10

= 54 x 10

540.

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21 2345
Q:

If the HCF of 210 and 55 is expressible in the form of 210 x 5 + 55P, then value of P = ?

A) -23 B) 27
C) 16 D) -19
 
Answer & Explanation Answer: D) -19

Explanation:

HCF of 210 and 55 is 5

Now, 210x5 + 55P = 5

=> 1050 + 55P = 5

=> 55P = -1045

=> P = -1045/55

=> P = -19.

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20 3255
Q:

A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is  ?

A) 63 B) 31
C) 16 D) 27
 
Answer & Explanation Answer: B) 31

Explanation:

To get the least number of coconuts :
LCM = 30 => 30 + 1 = 31

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23 4250
Q:

A drink vendor has 368 liters of Maaza, 80 liters of Pepsi and 144 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required ?

A) 47 B) 46
C) 37 D) 35
 
Answer & Explanation Answer: C) 37

Explanation:

The number of liters in each can = HCF of 80, 144 and 368 = 16 liters.
Number of cans of Maaza = 368/16 = 23
Number of cans of Pepsi = 80/16 = 5
Number of cans of Sprite = 144/16 = 9
The total number of cans required = 23 + 5 + 9 = 37 cans.

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24 3360
Q:

H.C.F of 4 x 27 x 3125, 8 x 9 x 25 x 7 and 16 x 81 x 5 x 11 x 49 is :

A) 360 B) 180
C) 90 D) 120
 
Answer & Explanation Answer: B) 180

Explanation:

4 x 27 x 3125 = 22 × 33 × 55 ;

 

8 x 9 x 25 x 7 = 23 × 32 × 52 × 7

 

16 x 81 x 5 x 11 x 49 = 24 × 34 × 5 × 11 × 72

 

H.C.F = 22 × 32 × 5 = 180.

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17 3124
Q:

The difference of two numbers is 14. Their LCM and HCF are 441 and 7. Find the two numbers ?

A) 63 and 49 B) 64 and 48
C) 62 and 46 D) 64 and 49
 
Answer & Explanation Answer: A) 63 and 49

Explanation:

Since their HCFs are 7, numbers are divisible by 7 and are of the form 7x and 7y

Difference = 14
=> 7x - 7y = 14
=> x - y = 2

product of numbers = product of their hcf and lcm
=> 7x * 7y = 441 * 7
=> x * y = 63

Now, we have
x * y = 63 , x - y = 2
=> x = 9 , y = 7

The numbers are 7x and 7y
=> 63 and 49

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18 7046