MCQ: HCF & LCM - 1 - SSC CGL MCQ

# MCQ: HCF & LCM - 1 - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: HCF & LCM - 1

MCQ: HCF & LCM - 1 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: HCF & LCM - 1 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: HCF & LCM - 1 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: HCF & LCM - 1 below.
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MCQ: HCF & LCM - 1 - Question 1

### The LCM of two numbers is 1920 and their HCF is 16. If one of the number is 128, find the other number.

Detailed Solution for MCQ: HCF & LCM - 1 - Question 1

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
We have,
First number × second number = LCM × HCF

MCQ: HCF & LCM - 1 - Question 2

### The HCF of two numbers is 15 and their LCM is 225. If one of the number is 75, then the other number is ?

Detailed Solution for MCQ: HCF & LCM - 1 - Question 2

First Number x Second Number = HCF x LCM
Then, 75 x Second Number = 15 x 225
Second Number latex ={ 15 x 225}/75 = 45\$
Therefore, other number is 45.

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MCQ: HCF & LCM - 1 - Question 3

### The L.C.M. of three different numbers is 120. Which of the following cannot be their H.C.F.?

Detailed Solution for MCQ: HCF & LCM - 1 - Question 3

We know that:
LCM is the least common multiple of the given numbers whereas HCF is the highest common factor of those numbers.
Then, LCM is the multiplication of one common factor of the numbers and the other different factors of the numbers.
Write the LCM = 120 into factored form, that is
120 = 2 × 2 × 2 × 3 × 5
= 4(2 × 3 × 5)
⇒ 4 is the common factor of the numbers.
So, the HCF of three numbers is a multiple of 4.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
Therefore, 35 is not the multiple of 4, then 35 cannot be their HCF.

MCQ: HCF & LCM - 1 - Question 4

The product of two numbers is 1280 and their H.C.F. is 8. The L.C.M. of the number will be ?

Detailed Solution for MCQ: HCF & LCM - 1 - Question 4

Product of two numbers = HCF × LCM
1280 = 8 × LCM
160 = LCM

MCQ: HCF & LCM - 1 - Question 5

The HCF and LCM of two numbers are 12 and 924 respectively. Then the number of such pairs is

Detailed Solution for MCQ: HCF & LCM - 1 - Question 5

The HCF and LCM of two numbers are 12 and 924.
Let the numbers be 12p and 12q where p and q are prime to each other.
∴ LCM = 12pq
∴ 12pq = 924
⇒ pq = 77
∴ Possible pairs are (1 , 77) and (7 ,11)
Hence , required answer is 2.

MCQ: HCF & LCM - 1 - Question 6

The product of two numbers is 2160 and their HCF is 12. Number of such possible pairs is

Detailed Solution for MCQ: HCF & LCM - 1 - Question 6

HCF = 12
Numbers = 12x and 12y
where x and y are prime to each other.
∴ 12x × 12y = 2160

= 15 = 3 × 5, 1 × 15
Possible pairs = (36, 60) and (12, 180)
Hence , Number of such possible pairs is 2.

MCQ: HCF & LCM - 1 - Question 7

LCM of two numbers is 225 and their HCF is 5. If one number is 25, the other number will be?

Detailed Solution for MCQ: HCF & LCM - 1 - Question 7

Given, LCM = 225, HCF = 5,
First Number = 25 , Second Number = ?
We can find the Second Number with the help of given formula,
"LCM × HCF = 1st Number× 2nd Number"
⇒ 225 × 5 = 25 × 2nd Number

∴ 2nd Number = 45

MCQ: HCF & LCM - 1 - Question 8

The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. The larger of the two numbers is :

Detailed Solution for MCQ: HCF & LCM - 1 - Question 8

HCF is 23. So the other two numbers would be,
(23 * 13) and (23 * 14).
Thus Larger Number = 23 * 14 = 322.

MCQ: HCF & LCM - 1 - Question 9

The H.C.F. of two numbers is 96 and their L.C.M. is 1296. If one of the number is 864, the other is

Detailed Solution for MCQ: HCF & LCM - 1 - Question 9

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × Second number = HCF × LCM
⇒ 864 × Second number
= 96 × 1296 ⇒ Second number

MCQ: HCF & LCM - 1 - Question 10

The LCM of two numbers is 1920 and their HCF is 16. If one of the number is 128, find the other number.

Detailed Solution for MCQ: HCF & LCM - 1 - Question 10

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
We have,
First number × second number = LCM × HCF

MCQ: HCF & LCM - 1 - Question 11

The HCF of two numbers is 15 and their LCM is 300. If one of the number is 60, the other is :

Detailed Solution for MCQ: HCF & LCM - 1 - Question 11

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
First number × Second number = HCF × LCM

MCQ: HCF & LCM - 1 - Question 12

The LCM of two numbers is 4 times their HCF. The sum of LCM and HCF is 125. If one of the number is 100, then the other number is

Detailed Solution for MCQ: HCF & LCM - 1 - Question 12

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
Let LCM be L and HCF be H, then L = 4H
∴ H + 4H = 125
⇒ 5H = 125

∴ L = 4 × 25 = 100

MCQ: HCF & LCM - 1 - Question 13

The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. The larger of the two numbers is :

Detailed Solution for MCQ: HCF & LCM - 1 - Question 13

Let the numbers be 23x and 23y where x and y are co-prime.
∴ LCM = 23 xy
As given,
23xy = 23 × 13 × 14
∴ x = 13, y = 14
∴ The larger number = 23y
= 23 × 14 = 322

MCQ: HCF & LCM - 1 - Question 14

The HCF and LCM of two numbers are 13 and 455 respectively. If one of the number lies between 75 and 125, then, that number is :

Detailed Solution for MCQ: HCF & LCM - 1 - Question 14

HCF = 13
Let the numbers be 13x and 13y.
Where x and y are co-prime.
∴ LCM = 13 xy
∴ 13 xy = 455

∴ Numbers are 13 × 5 = 65 and 13 × 7 = 91

MCQ: HCF & LCM - 1 - Question 15

The LCM of two numbers is 864 and their HCF is 144. If one of the number is 288, the other number is :

Detailed Solution for MCQ: HCF & LCM - 1 - Question 15

Using Rule 1 :
1st number × 2nd number = L.C. M. × H.C.F,
Required number

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## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests