LCM and HCF
 The HCF of two numbers is 16 and their LCM is 160. If one of the number is 32, then the other number is

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Given ,LCM = 160 , HCF = 16 , First number = 32 , Second number = ?
We know that,
First number × Second number = LCM × HCFCorrect 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
 The H.C.F. and L.C.M. of two 2digit numbers are 16 and 480 respectively. The numbers are :

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Given that ,
L.C.M. of the two 2digit numbers = 480
H.C.F. of the two 2digit 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 2digit numbers = 480
H.C.F. of the two 2digit 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 2digits 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
 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
 The LCM of two numbers is 1920 and their HCF is 16. If one of the number is 128, find the other number.

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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
 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 :

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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 numberCorrect 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