## LCM and HCF

#### LCM and HCF

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

1. Given that , Product of two numbers = 1280
HCF = 8 , LCM = ?
We can find LCM with the help of the given formula ,
HCF × LCM = Product of two numbers
⇒ 8 × LCM = 1280

##### Correct Option: A

Given that , Product of two numbers = 1280
HCF = 8 , LCM = ?
We can find LCM with the help of the given formula ,
HCF × LCM = Product of two numbers
⇒ 8 × LCM = 1280

 ⇒ LCM = 1280 = 160 8

1. The LCM of two numbers is 30 and their HCF is 5. One of the number is 10. The other is

1. Here , LCM = 30 , HCF = 5 , First number = 10, Second number = 14818
As we know that ,
First number × second number = LCM × HCF
Let the second number be p.
∴ 10p = 30 × 5

 ⇒ p = 30 × 5 10

##### Correct Option: C

Here , LCM = 30 , HCF = 5 , First number = 10, Second number = 14818
As we know that ,
First number × second number = LCM × HCF
Let the second number be p.
∴ 10p = 30 × 5

 ⇒ p = 30 × 5 = 15 10

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

1. Here , 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

##### Correct Option: C

Here , 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 = ( 1 , 77 ) and ( 7 ,11 )
Hence , required answer is 2.

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

1. Given that , LCM = 300 , HCF = 15 , First number = 60 , Second number = ?
With the help of the given formula ,
First number × Second number = HCF × LCM

 ∴ Second number = 15 × 300 60

##### Correct Option: B

Given that , LCM = 300 , HCF = 15 , First number = 60 , Second number = ?
With the help of the given formula ,
First number × Second number = HCF × LCM

 ∴ Second number = 15 × 300 = 75 60

1. The product of two numbers is 4107. If the H.C.F. of the numbers is 37, the greater number is

1. We can find required answer with the help of given formula ,

 LCM = Product of two numbers HCF

 LCM = 4107 = 111 37

##### Correct Option: B

We can find required answer with the help of given formula ,

 LCM = Product of two numbers HCF

 LCM = 4107 = 111 37

Obviously, numbers are 111 and 37 which satisfy the given condition.
Hence, the greater number = 111