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The HCF of two numbers is 9. Which one of the following can never of their LCM?
- A27
- B45
- C54
- D60
Answer not set
Discussion 1
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CCommunity
H.C.F of two numbers is the highest factor present in both the numbers.
So we can say, if the HCF of two numbers is 9 then the two numbers can be 9x & 9y where x & y are co-prime.
The LCM of these two numbers = product of these two numbers
[Because co-prime numbers don’t have any common factors other than 1]
So, LCM of 9x & 9y = 9xy [Only one 9 in the LCM because it’s a common factor of both the numbers]
∴We can conclude that the LCM must be an integral multiple of 9 as x & y are integers.
From the options given only 60 is the number which is not an integral multiple of 9. So it can never be the LCM.
So we can say, if the HCF of two numbers is 9 then the two numbers can be 9x & 9y where x & y are co-prime.
The LCM of these two numbers = product of these two numbers
[Because co-prime numbers don’t have any common factors other than 1]
So, LCM of 9x & 9y = 9xy [Only one 9 in the LCM because it’s a common factor of both the numbers]
∴We can conclude that the LCM must be an integral multiple of 9 as x & y are integers.
From the options given only 60 is the number which is not an integral multiple of 9. So it can never be the LCM.