LCM and HCF
 The HCF and LCM of two numbers are 18 and 378 respectively. If one of the number is 54, then the other number is

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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
 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 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 HCF and product of two numbers are 15 and 6300 respectively. The number of possible pairs of the numbers is

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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.
 The H.C.F. of two numbers is 96 and their L.C.M. is 1296. If one of the number is 864, the other is

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Here , LCM = 1296 , HCF = 96 , First number = 864 , Second number = ?
As We know that ,
First number × Second number = HCF × LCM
⇒ 864 × Second number = 96 × 1296Correct Option: D
Here , LCM = 1296 , HCF = 96 , First number = 864 , Second number = ?
As We know that ,
First number × Second number = HCF × LCM
⇒ 864 × Second number = 96 × 1296⇒ Second number = 96 × 1296 = 144 864