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# if the hcf of two numbers is 9, then which of the following can never be their lcm?

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### Mohammed

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## The HCF of two numbers is 9. Which one can’t be their LCM?a)24b)36c)54d)48Correct answer is option 'D'. Can you explain this answer?

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 and9y where x andy are co-prime.The LCM of these two numbers = product of these two numbers.So, LCM of 9x and 9y = 9xy (Only one 9 in the LCM because it is a common factor of both the numbers).Hence, we can conclude that the LCM must be an integral multiple of 9 as x and y are integers. From the options given only 48is the number which is not an integral multiple of 9. So it can never be the LCM.

Class 5 Question  >  The HCF of two numbers is 9. Which one can&rs...

The HCF of two numbers is 9. Which one can’t be their LCM?

a) 24 b) 36 c) 54 d) 48

### Related Test

Test: HCF & LCM- 2

Rahul Kumar Sep 16, 2021 Related

The HCF of two numbers is 9. Which one can’t be their LCM?a)24b)36c)54d)48Correct answer is option 'D'. Can you explain this answer?

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 and 9y where x and y are co-prime.

The LCM of these two numbers = product of these two numbers.

So, LCM of 9x and 9y = 9xy (Only one 9 in the LCM because it is a common factor of both the numbers).

Hence, we can conclude that the LCM must be an integral multiple of 9 as x and y are integers.

From the options given only 48 is the number which is not an integral multiple of 9. So it can never be the LCM.

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## The HCF of two numbers is 9. Which one of the following can never of their LCM?

The HCF of two numbers is 9. Which one of the following can never of their LCM?
1). 27
2). 45
3). 54
4). 60 The HCF of two numbers is 9. Which one of the following can never of their LCM?

38 vote

## The HCF of two numbers is 9. Which one of the following can never of their LCM?

Asked on      2019-06-10 12:40:04 by Guest | Votes 38 | Views: 3398 | Tags: number system     | quantitative aptitude     | Add Bounty

The HCF of two numbers is 9. Which one of the following can never of their LCM?

1). 27 2). 45 3). 54 4). 60

27 vote

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.

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## If the HCF of two numbers is 9, what is their LCM?

Answer (1 of 3): That depends on the numbers. They could be 9 and 27, in which case the LCM is 27. They could be 36 and 45, in which case the LCM is 180. In general, if the HCF of two numbers is 9, then that means they must be divisible by 9, so let’s call the numbers 9*a and 9*b, where a and ...

If the HCF of two numbers is 9, what is their LCM?

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Sort Ari Mermelstein

BS and MA in Computer Science & Mathematics, Brooklyn College (public college)Author has 1.2K answers and 918.2K answer views5y

We know that: LCM(a,b)= ab HCF(a,b) LCM(a,b)=abHCF(a,b)

unfortunately, you've only supplied one variable, so there isn't a unique answer.

For example, HCF(9,18)=9. HCF(9,18)=9. In this case, LCM(9,18)= 18×9 9 =18. LCM(9,18)=18×99=18.

But, this isn't a unique answer.

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What will be the LCM of two numbers if their HCF is 1?

The product of two numbers is 81. If their LCM is 9, what is their HCF?

Emmeryn Gelblicht

That depends on the numbers.

They could be 9 and 27, in which case the LCM is 27.

They could be 36 and 45, in which case the LCM is 180.

In general, if the HCF of two numbers is 9, then that means they must be divisible by 9, so let’s call the numbers 9*a and 9*b, where a and b are both integers (so 1, 2, 3), except they can’t share any prime factors, since otherwise the LCM wouldn’t be 9.

For 9 and 27, a=1 and b=3. For 36 and 45, a=4 and b=5.

The LCM is 9*a*b

(Note that a and b are interchangeable.)

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If the HCF of two numbers is 2 and their product is 120, what is their LCM?

HCF = 2

Product of 2 no:s = 120

LCM = x

We know that , HCF × LCM = Product of 2 no:s

2x = 120 x = 120/2 x = 60 LCM = x = 60 Aanya 1y Related

The HCF of two numbers is 2 and their product is 56. What will be the LCM?

Formula = H.C.F ×L.C.M= Product of two numbers

2× L.C.M =56 L.C.M = 56÷2 L.C.M =28 .

Manjunath Subramanya Iyer

I am a retired bank officer teaching mathsAuthor has 7.2K answers and 7.7M answer views5y

If you give only HCF then the LCM will not be unique.

For example, 9 and 18 have HCF 9 and their LCM is 18

But if you take the numbers 9 and 27 their HCF is also 9, but their LCM is 27 !

We can give many more examples like this !

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CMA K S Narayanan

Cost Accountant having 24 years Telecom ExperienceAuthor has 6.1K answers and 10M answer views5y

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Two numbers have an LCM of 20 and an HCF of 4. What are they?

Let 4a & 4b be the two numbers where a & b are co-primes.

Now LCM x HCF = Product of numbers

=> 20 x 4 = 16ab => ab = 5

The only possible integer values of a & b is a=1 & b= 5 or a= 5 & b = 1

So, the required numbers are 4 and 20.

Eliyahu Peter Kornfeld

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What two numbers have the LCM of 24 and the HCF of 2?

Least common multiple (LCM)…

First see all the divisors of 24: 2, 3, 4, 6, 8, 12, 24

The possible pair form that are (order is irrelevant):

2, 3 (LCM = 6) 2, 4 (LCM = 4) 2, 6 (LCM = 6) 2, 8 (LCM = 8) 2, 12 (LCM = 12) 2, 24 (LCM = 24) 3, 4 (LCM = 12) 3, 6 (LCM = 6) 3, 8 (LCM = 24) 3, 12 (LCM = 12) 3, 24 (LCM = 24) 4, 6 (LCM = 12) 4, 8 (LCM = 8) 4, 12 (LCM = 12) 4, 24 (LCM = 24) 6, 8 (LCM = 24) 6, 12 (LCM = 12) 6, 24 (LCM = 24) 8, 12 (LCM = 24) 8, 24 (LCM = 24) 12, 24 (LCM = 24)

The possible answers are in bold…

Greatest common divisor (GCD === HCF)

2, 24 (GCD = 2) 3, 8 (GCD = 1) 3, 24 (GCD = 3) 4, 24 (GCD = 4) 6, 8 (GCD = 2

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If the HCF of two numbers is 15, what is their LCM?

This question is incomplete-

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The product of two numbers is 81. If their LCM is 9, what is their HCF?

LCM×HCF=product of the two numbers

LCM×HCF=product of the two numbers

∴HCF= 81 9 =9 ∴HCF=819=9 Sponsored by Sirv

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Mohammed 1 month ago

Guys, does anyone know the answer?