## LCM and HCF

#### LCM and HCF

1. The HCF and LCM of two numbers are 18 and 378 respectively. If one of the number is 54, then the other number is

1. Given , LCM = 378 , HCF = 18 , First number = 54 , Second number = ?
As We know that ,

 Second number = HCF × LCM First number

##### Correct Option: A

Given , LCM = 378 , HCF = 18 , First number = 54 , Second number = ?
As We know that ,

 Second number = HCF × LCM First number

 Second number = 18 × 378 = 126 54

1. The LCM of two numbers is 520 and their HCF is 4. If one of the number is 52, then the other number is

1. Given that , LCM = 520 , HCF = 4 , First number = 52, Second number = ?
We can find other number with the help of the given formula ,
First number × second number = HCF × LCM
⇒ 52 × second number = 4 × 520

##### Correct Option: A

Given that , LCM = 520 , HCF = 4 , First number = 52, Second number = ?
We can find other number with the help of the given formula ,
First number × second number = HCF × LCM
⇒ 52 × second number = 4 × 520

 ⇒ Second number = 4 × 520 = 40 52

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

1. Given , LCM = 225 , HCF = 15 , First number = 75 , Second number = ?
As We know that ,
First number × Second number = HCF × LCM
⇒ 75 × Second number = 15 × 225

 ∴ Second number = 15 × 225 75

##### Correct Option: D

Given , LCM = 225 , HCF = 15 , First number = 75 , Second number = ?
As We know that ,
First number × Second number = HCF × LCM
⇒ 75 × Second number = 15 × 225

 ∴ Second number = 15 × 225 = 45 75

1. The HCF and product of two numbers are 15 and 6300 respectively. The number of possible pairs of the numbers is

1. Here , HCF = 15
Let the number be 15p and 15q, where p and q are co – prime.
With the help of the given formula ,
HCF × LCM = Product of two numbers
∴ 15p × 15q = 6300

 ⇒ pq = 6300 = 28 15 × 15

##### Correct Option: C

Here , HCF = 15
Let the number be 15p and 15q, where p and q are co – prime.
With the help of the given formula ,
HCF × LCM = Product of two numbers
∴ 15p × 15q = 6300

 ⇒ pq = 6300 = 28 15 × 15

So, two pairs are ( 7 , 4 ) and ( 14 , 2 ) .
Hence , required answer is 2.

1. 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

1. Here , LCM = 1296 , HCF = 96 , First number = 864 , Second number = ?
As We know that ,
First number × Second number = HCF × LCM
⇒ 864 × Second number = 96 × 1296

##### Correct Option: D

Here , LCM = 1296 , HCF = 96 , First number = 864 , Second number = ?
As We know that ,
First number × Second number = HCF × LCM
⇒ 864 × Second number = 96 × 1296

 ⇒ Second number = 96 × 1296 = 144 864