## LCM and HCF

#### LCM and HCF

1. Product of two co-prime numbers is 117. Then their L.C.M. is

1. HCF of two-prime numbers = 1
As we know that ,
Product of numbers = LCM × HCF
∴ Product of numbers = LCM × 1 = 117
Their LCM = 117 = 13 × 9 , where 13 & 9 are co-prime.

##### Correct Option: A

HCF of two-prime numbers = 1
As we know that ,
Product of numbers = LCM × HCF
∴ Product of numbers = LCM × 1 = 117
Their LCM = 117 = 13 × 9 , where 13 & 9 are co-prime.
L.C.M ( 13 , 9 ) = 117.

1. 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

1. Let LCM be L and HCF be H, then
According to question ,
L = 4H
sum of LCM and HCF = 125
⇒ H + 4H = 125
⇒ 5H = 125

 ⇒ H = 125 = 25 5

∴ L = 4 × 25 = 100

##### Correct Option: B

Let LCM be L and HCF be H, then
According to question ,
L = 4H
sum of LCM and HCF = 125
⇒ H + 4H = 125
⇒ 5H = 125

 ⇒ H = 125 = 25 5

∴ L = 4 × 25 = 100
 ∴ Second number = L × H First number

 Second number = 100 × 25 = 25 100

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

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