LCM and HCF
 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 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 product of two numbers is 216. If the HCF is 6, then their LCM is

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Let the numbers be 6p and 6q where p and q are prime to each other.
∴ 6p × 6q = 216⇒ pq = 216 = 6 6 × 6
Correct Option: D
Let the numbers be 6p and 6q where p and q are prime to each other.
∴ 6p × 6q = 216⇒ pq = 216 = 6 6 × 6
∴ LCM = 6pq = 6 × 6 = 36
 The H.C.F and L.C.M of two numbers are 12 and 336 respectively. If one of the number is 84, the other is

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Here , LCM = 336 , HCF = 12 , First number = 84, Second number = ?
We can find other number with the help of the given formula ,
First number × second number = HCF × LCM
⇒ 84 × second number = 12 × 336Correct Option: B
Here , LCM = 336 , HCF = 12 , First number = 84, Second number = ?
We can find other number with the help of the given formula ,
First number × second number = HCF × LCM
⇒ 84 × second number = 12 × 336∴ Second number = 12 × 336 = 48 84
 The HCF of two numbers 12906 and 14818 is 478. Their LCM is

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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 × 478Correct 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