LCM and HCF Both MCQ Quiz - Objective Question with Answer for LCM and HCF Both - Download Free PDF

Given:

Numbers: 64 and b

LCM = 160

HCF = 16

Formula used:

LCM × HCF = Product of the numbers

Calculation:

160 × 16 = 64 × b

⇒ 160 = 4 × b

⇒ b = 40

∴ The correct answer is option (4).

Given:

LCM = 160

HCF = 16

First Number = 64

Second Number = x

Formula used:

Product of two numbers = LCM × HCF

Calculation:

(64 × x) = (LCM × HCF)

⇒ (64 × x) = 2560

⇒ \(x = \dfrac{2560}{64}\)

⇒ x = 40

∴ The correct answer is option 1.

Given:

The H.C.F. of two numbers = 29

Other two divisors of their Least Common Multiple (LCM) = 15 and 16

Formula used:

LCM = HCF × Product of other divisors

Smallest number = HCF × One divisor

Calculations:

LCM = 29 × 15 × 16

⇒ LCM = 6960

Smallest number = HCF × One divisor

⇒ Smallest number = 29 × 15

⇒ Smallest number = 435

∴ The correct answer is option (2).

Given:

HCF of two numbers = 29

Two divisors of LCM = 23 and 25

Calculation:

As we know, HCF is a factor of LCM.

LCM = 29 × 23 × 25

First number = 29 × 23 = 667

Second number = 29 × 25 = 725

Therefore, the largest number among them is 725.

Given:

LCM of two numbers = 168

HCF of two numbers = 6

One of the numbers = 24

Formula Used:

Product of two numbers = LCM × HCF

Let the other number be x, then:

Number 1 × Number 2 = LCM × HCF

Calculation:

Given Number 1 = 24, let Number 2 = x

⇒ 24 × x = 168 × 6

⇒ x = (168 × 6) / 24

⇒ x = 1008 / 24

⇒ x = 42

The other number is 42.

Given:

LCM = 48

Product of the numbers = 384

Concept used:

LCM × HCF = The Product of two numbers

Calculation:

​According to the concept,

HCF = 384/48 = 8

HCF : LCM = 8 : 48 = 1 : 6

∴ The ratio between the HCF and LCM is 1 : 6.

Calculations:

Let a and b be two numbers.

We know (H.C.F) × (L.C.M) = Product of two numbers

Putting H.C.F and L.C.M. as 3 and 54 respectively we get a × b = 3 × 54

Also, a + b = 18

So, we have 

1/a + 1/b

⇒ (a + b)/ab

⇒ 18/(3 × 54)

  =   1/9

Hence, The Required value is 1/9.

Given:

The HCF of two numbers is 12. 

Concept used:

1. If P is the HCF of A and B then, A = P × m and B = P × n.

2. LCM is the smallest common multiple of two or more numbers.

Calculation:

Let the ratio of two numbers be A : B and their HCF be H and LCM be L.

Then, the numbers are AH and BH respectively.

LCM (AH, BH) i.e. L = H × A × B

Hence, L is a multiple of H.

Accordingly, if the HCF of two numbers is 12, then their LCM has to be multiple of 12.

Hence, 90 can't be their LCM.

∴ 90 can never be their LCM.

Given:

Two numbers are in the ratio of 6 ∶ 5.

Their HCF is 3.

Concept used:

1. If P is the HCF of A and B then A = P × m & B = P × n. (Where m and n are arbitrary positive integers and they are co-prime to each other)

2. LCM is the smallest common multiple of two or more numbers.

Calculation:

First number = 6 × 3 = 18

Second number = 5 × 3 = 15

LCM (18, 15) = 3 × 6 × 5 = 90

∴  Their LCM is 90.

Given:

The numbers are in the ratio of 2 : 3 : 5

LCM of the numbers = 90

Calculation:

Let the number be 2x, 3x and 5x.

LCM of (2x, 3x and 5x) = 2 × 3 × 5 × (x)

⇒ 30x

According to the question, 30x = 90

⇒ x = 90/30

⇒ x = 3

So, the numbers are 6, 9, 15

Now,

6 = 2 × 3

9 = 3²

15 = 3 × 5 

So, HCF = 3

∴ The H.C.F. of the three numbers is 3.

Given:

The HCF of the two numbers is 17 and the other two factors of their LCM are 11 and 19.

Concept used:

If the HCF of two numbers is H and the other two factors of their LCM are A and B, then the numbers are AH and BH respectively.

Calculation:

Smaller number = 17 × 11 = 187

∴ The smaller of the two numbers is 187.

Calculation:

Let the two numbers be 5x and 4x

As we know,

LCM of 5x and 4x= 20x

HCF of 5x and 4x = x = 4

According to the question

20x = 20 × 4 = 80

∴ The LCM of the two numbers is 80.

Given:

LCM = 4104 , HCF = 9, one of the number = 171

Concept used:

LCM × HCF = Product of the numbers

Calculations:

LCM × HCF = Product of the numbers

⇒ 4104 × 9 = 171 × other number

⇒ other number = 4104 × 9/171 = 216

Hence, The Required value is 216.

Given:

The ratio of two numbers is 6 ∶ 7 and their HCF is 3. 

Concept used:

LCM is the smallest common multiple of two or more numbers.

Calculation:

First number = 6 × 3 = 18

Second number = 7 × 3 = 21

LCM (18, 21) = 3 × 6 × 7 = 126

∴ Their LCM is 126.

Given:

HCF is 9 and their ratio is 14 : 19.

Concept used:

1. LCM is the smallest common multiple of two or more numbers.

2. HCF is the largest number or quantity that is a factor of each member of a group of numbers.

Calculation:

First number = 14 × 9 = 126

Second number = 19 × 9 = 171

LCM (126, 171)

⇒ 9 × 14 × 19

⇒ 2394

∴ Their LCM is 2394.