LCM and HCF
- The H.C.F. and L.C.M. of two 2-digit numbers are 16 and 480 respectively. The numbers are :
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Given that ,
L.C.M. of the two 2-digit numbers = 480
H.C.F. of the two 2-digit 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 2-digit numbers = 480
H.C.F. of the two 2-digit 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 2-digits 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 and LCM of two numbers are 12 and 924 respectively. Then the number of such pairs is
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Here , HCF and LCM of two numbers are 12 and 924 .
Let the numbers be 12p and 12q where p and q are prime to each other.
∴ LCM = 12pq
∴ 12pq = 924
⇒ pq = 77Correct Option: C
Here , HCF and LCM of two numbers are 12 and 924 .
Let the numbers be 12p and 12q where p and q are prime to each other.
∴ LCM = 12pq
∴ 12pq = 924
⇒ pq = 77
∴ Possible pairs = ( 1 , 77 ) and ( 7 ,11 )
Hence , required answer is 2.
- The product of two numbers is 1280 and their H.C.F. is 8. The L.C.M. of the number will be :
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Given that , Product of two numbers = 1280
HCF = 8 , LCM = ?
We can find LCM with the help of the given formula ,
HCF × LCM = Product of two numbers
⇒ 8 × LCM = 1280Correct Option: A
Given that , Product of two numbers = 1280
HCF = 8 , LCM = ?
We can find LCM with the help of the given formula ,
HCF × LCM = Product of two numbers
⇒ 8 × LCM = 1280⇒ LCM = 1280 = 160 8
- The LCM of two numbers is 30 and their HCF is 5. One of the number is 10. The other is
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Here , LCM = 30 , HCF = 5 , First number = 10, Second number = 14818
As we know that ,
First number × second number = LCM × HCF
Let the second number be p.
∴ 10p = 30 × 5⇒ p = 30 × 5 10 Correct Option: C
Here , LCM = 30 , HCF = 5 , First number = 10, Second number = 14818
As we know that ,
First number × second number = LCM × HCF
Let the second number be p.
∴ 10p = 30 × 5⇒ p = 30 × 5 = 15 10
- The H.C.F. of two numbers is 8. Which one of the following can never be their L.C.M.?
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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
