LCM and HCF
 The HCF of two numbers is 15 and their LCM is 225. If one of the number is 75, then the other number is :

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Given , LCM = 225 , HCF = 15 , First number = 75 , Second number = ?
As We know that ,
First number × Second number = HCF × LCM
⇒ 75 × Second number = 15 × 225∴ Second number = 15 × 225 75 Correct Option: D
Given , LCM = 225 , HCF = 15 , First number = 75 , Second number = ?
As We know that ,
First number × Second number = HCF × LCM
⇒ 75 × Second number = 15 × 225∴ Second number = 15 × 225 = 45 75
 The LCM of two numbers is 520 and their HCF is 4. If one of the number is 52, then the other number is

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Given that , LCM = 520 , HCF = 4 , First number = 52, Second number = ?
We can find other number with the help of the given formula ,
First number × second number = HCF × LCM
⇒ 52 × second number = 4 × 520Correct Option: A
Given that , LCM = 520 , HCF = 4 , First number = 52, Second number = ?
We can find other number with the help of the given formula ,
First number × second number = HCF × LCM
⇒ 52 × second number = 4 × 520⇒ Second number = 4 × 520 = 40 52
 The product of two numbers is 2028 and their HCF is 13. The number of such pairs is

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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 coprime.
∴ The required no. of pairs = 2
 LCM of two numbers is 2079 and their HCF is 27. If one of the number is 189, the other number is

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

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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.