## LCM and HCF

#### LCM and HCF

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 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 product of two numbers is 216. If the HCF is 6, then their LCM is

1. Let the numbers be 6p and 6q where p and q are prime to each other.
∴ 6p × 6q = 216

 ⇒ pq = 216 = 6 6 × 6

##### Correct Option: D

Let the numbers be 6p and 6q where p and q are prime to each other.
∴ 6p × 6q = 216

 ⇒ pq = 216 = 6 6 × 6

∴ LCM = 6pq = 6 × 6 = 36

1. The H.C.F and L.C.M of two numbers are 12 and 336 respectively. If one of the number is 84, the other is

1. Here , LCM = 336 , HCF = 12 , First number = 84, Second number = ?
We can find other number with the help of the given formula ,
First number × second number = HCF × LCM
⇒ 84 × second number = 12 × 336

##### Correct Option: B

Here , LCM = 336 , HCF = 12 , First number = 84, Second number = ?
We can find other number with the help of the given formula ,
First number × second number = HCF × LCM
⇒ 84 × second number = 12 × 336

 ∴ Second number = 12 × 336 = 48 84

1. The HCF of two numbers 12906 and 14818 is 478. Their LCM is

1. Here , LCM = ? , HCF = 478 , First number = 12906, Second number = 14818
With the help of the given formula ,
Product of two numbers = HCF × LCM
⇒ 12906 × 14818 = LCM × 478

##### Correct Option: A

Here , LCM = ? , HCF = 478 , First number = 12906, Second number = 14818
With the help of the given formula ,
Product of two numbers = HCF × LCM
⇒ 12906 × 14818 = LCM × 478

 ⇒ LCM = 12906 × 14818 = 400086 478