Highest Common Factor And Least Common Multiple MCQ Set 9

Showing question 41 to 45 of total 54 MCQs

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Question No: 41

Rajesh had to arrange his books in uniform groups. He makes groups of 4 books each. But 3 books are left. He tries it with groups of 5 books each. But still 3 books are left. 3 books are still left when he tried with groups of 9 or 10 books each. How many books does he have?

1. 90
2. 180
3. 900
4. 183

Answer: D

Explanation

Since we need total number of books, we must first find LCM of 4, 5, 9, 10

LCM = 2 × 5 × 2 × 1 × 9 × 1= 180

Since remainder is same i.e. 3 books, just add it to this LCM

Number of books = 180 + 3 = 183

Question No: 42

HCF and LCM of two numbers is 8 and 96. Sum of those numbers is 56. Then what is sum of their reciprocals?

1. 1/56
2. 7/96
3. 1/96
4. 1/8

Answer: C

Explanation

If A and B are two numbers,

A × B = HCF of A and B × LCM of A and B

Let numbers be P and Q

Also, P + Q = 56 and PQ = HCF × LCM = 8 × 96

Question No: 43

What is LCM of 36/225, 48/150 , 72/65 ?

1. 36/65
2. 144/5
3. 72/225
4. 288/5

Answer: B

Explanation

Numerators = 36, 48 and 72

72 is largest number among them. 72 is not divisible by 36 or 48

start with table of 72.

72 × 2 = 144 = divisible by 72, 36 and 48

LCM of numerators = 144

Denominators = 225, 150 and 65

We can see that they can be divided by 5.

On dividing by 5 we get 45, 30 and 13

We cannot divide further.

so HCF = GCD = 5

LCM of fraction = 144/5

Question No: 44

Idrees wants to paste wallpaper on wall of his room. The wall is 4 meters and 50 cm in length and 3 meters and 50 cm in height. But the wall should be covered completely only by square pieces of wallpaper having same size. What is the number of maximum sized wallpaper squares needed to cover the walls completely?

1. 8
2. 15.75
3. 63
4. 12

Answer: C

Explanation

Wall can be covered only by using square sized wallpaper pieces.

Different sized squares are not allowed.

Length = 4m 50cm = 450cm; Height = 3m 50cm = 350cm

Maximum square size of possible means HCF of 350 and 450

We can see that 350 and 450 can be divided by 50.

On dividing by 50, we get 7 and 9.

Since we cannot divide further, HCF = 50 = size side of square

Question No: 45

The ratio of two numbers is 5 : 6 and their LCM is 480, then their HCF is?

1. 16
2. 96
3. 12
4. 240