## LCM and HCF

#### LCM and HCF

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. 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 L.C.M. of two numbers is 1820 and their H.C.F. is 26. If one number is 130 then the other number is :

1. Given that , L.C.M. of two numbers = 1820
H.C.F. of those numbers = 26
One of the number is 130
As we know that ,
LCM × HCF = First number × Second number

##### Correct Option: C

Given that
L.C.M. of two numbers = 1820
H.C.F. of those numbers = 26
One of the number is 130
As we know that ,
LCM × HCF = First number × Second number

 ∴ Another number = 1820 × 130 = 45 364