## LCM and HCF

#### LCM and HCF

1. The H.C.F. and L.C.M. of two 2-digit numbers are 16 and 480 respectively. The numbers are :

1. Given that ,
L.C.M. of the two 2-digit numbers = 480
H.C.F. of the two 2-digit numbers = 16
Hence, the numbers can be expressed as 16p and 16q, where p and q are prime to each other.
As we know that ,
First number × second number = H.C.F. × L.C.M.
⇒ 16p × 16q = 16 × 480

 ⇒ pq = 16 × 480 = 30 16 × 16

##### Correct Option: D

Given that ,
L.C.M. of the two 2-digit numbers = 480
H.C.F. of the two 2-digit numbers = 16
Hence, the numbers can be expressed as 16p and 16q, where p and q are prime to each other.
As we know that ,
First number × second number = H.C.F. × L.C.M.
⇒ 16p × 16q = 16 × 480

 ⇒ pq = 16 × 480 = 30 16 × 16

The possible pairs of p and q, satisfying the condition pq = 30 are :- (3, 10), (5, 6), (1, 30), (2, 15)
Since the numbers are of 2-digits each.
Hence, admissible pair is (5, 6)
i.e. p = 5 and q = 6
∴ Numbers are : 16p = 16 × 5 = 80 and 16q = 16 × 6 = 96

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

1. The LCM of two numbers is 1920 and their HCF is 16. If one of the number is 128, find the other number.

1. Given ,LCM = 1920 , HCF = 16 , First number = 128 , Second number = ?
As We know that ,
First number × second number = LCM × HCF

 ∴ Second number = LCM × HCF First number

##### Correct Option: B

Given ,LCM = 1920 , HCF = 16 , First number = 128 , Second number = ?
As We know that ,
First number × second number = LCM × HCF

 ∴ Second number = LCM × HCF First number

 ∴ Second number = 1920 × 16 = 45 240

1. The HCF of two numbers is 16 and their LCM is 160. If one of the number is 32, then the other number is

1. Given ,LCM = 160 , HCF = 16 , First number = 32 , Second number = ?
We know that,
First number × Second number = LCM × HCF

##### Correct Option: B

Given ,LCM = 160 , HCF = 16 , First number = 32 , Second number = ?
We know that,
First number × Second number = LCM × HCF

 ⇒ Second number = 16 × 160 = 80 32

1. LCM of two numbers is 225 and their HCF is 5. If one number is 25, the other number will be:

1. Given , LCM = 225 , HCF = 5 , First Number = 25 , Second Number = ?
We can find the Second Number with the help of given formula ,
LCM × HCF = 1st Number× 2nd Number
⇒ 225 × 5 = 25 × 2nd Number

##### Correct Option: C

Given , LCM = 225 , HCF = 5 , First Number = 25 , Second Number = ?
We can find the Second Number with the help of given formula ,
LCM × HCF = 1st Number× 2nd Number
⇒ 225 × 5 = 25 × 2nd Number

 2nd Number = 225 × 5 = 45 25