## LCM and HCF

#### LCM and HCF

1. The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M.?

1. Here , HCF of two numbers is 8.
This means 8 is a factor common to both the numbers. LCM is common multiple for the two numbers, it is divisible by the two numbers.

##### Correct Option: D

Here , HCF of two numbers is 8.
This means 8 is a factor common to both the numbers. LCM is common multiple for the two numbers, it is divisible by the two numbers. So, the required answer = 60

1. The HCF and LCM of two numbers are 13 and 455 respectively. If one of the number lies between 75 and 125, then, that number is :

1. Given that , HCF = 13 , LCM = 455
Let the numbers be 13p and 13q , Where p and q are co-prime.
∴ LCM = 13pq
∴ 13pq = 455

 ∴ pq = 455 13

##### Correct Option: B

Given that , HCF = 13 , LCM = 455
Let the numbers be 13p and 13q , Where p and q are co-prime.
∴ LCM = 13pq
∴ 13pq = 455

 ∴ pq = 455 = 35 = 5 × 7 13

∴ Numbers are 13 × 5 = 65 and 13 × 7 = 91

1. The product of two numbers is 2028 and their HCF is 13. The number of such pairs is

1. Here, HCF = 13
Let the numbers be 13p and 13q ,where p and q are Prime to each other.
Now, 13p × 13q = 2028

 ⇒ pq = 2028 = 12 13 × 13

##### Correct Option: B

Here, HCF = 13
Let the numbers be 13p and 13q ,where p and q are Prime to each other.
Now, 13p × 13q = 2028

 ⇒ pq = 2028 = 12 13 × 13

The possible pairs are :- ( 1 , 12 ) , ( 3 , 4 ) , ( 2 , 6 )
But the 2 and 6 are not co-prime.
∴ The required no. of pairs = 2

1. LCM of two numbers is 2079 and their HCF is 27. If one of the number is 189, the other number is

1. Here , LCM = 2079 , HCF = 27 , First number = 189, Second number = ?
We can find other number with the help of the given formula ,

 Second number = H.C.F. × L.C.M. First Number

##### Correct Option: A

Here , LCM = 2079 , HCF = 27 , First number = 189, Second number = ?
We can find other number with the help of the given formula ,

 Second number = H.C.F. × L.C.M. First Number

 Second number = 27 × 2079 = 297 189

1. The product of two numbers is 2160 and their HCF is 12. Number of such possible pairs is

1. Given that , HCF = 12
Let Numbers are 12p and 12q , where p and q are prime to each other.
∴ 12p × 12q = 2160

 ⇒ pq = 2160 = 15 12 × 12

##### Correct Option: B

Given that , HCF = 12
Let Numbers are 12p and 12q , where p and q are prime to each other.
∴ 12p × 12q = 2160

 ⇒ pq = 2160 = 15 12 × 12

Possible Factors of 15 = 3 × 5, 1 × 15
So , Possible pairs = ( 36 , 60 ) and ( 12 , 180 ) .
Hence , Number of such possible pairs is 2.