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# If the product of two positive integers is 144, which of the following

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Math Expert
Joined: 02 Sep 2009
Posts: 62287
If the product of two positive integers is 144, which of the following  [#permalink]

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09 Mar 2016, 11:44
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Difficulty:

65% (hard)

Question Stats:

60% (02:04) correct 40% (01:28) wrong based on 189 sessions

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If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers?

I. LCM : 24; HCF : 6
II. LCM : 18; HCF : 8
III. LCM : 16; HCF : 9

A. I only
B. II and III only
C. I and II only
D. I and III only
E. I, II and III

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Posts: 1865
Re: If the product of two positive integers is 144, which of the following  [#permalink]

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09 Mar 2016, 20:49
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Bunuel wrote:
If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers?

I. LCM : 24; HCF : 6
II. LCM : 18; HCF : 8
III. LCM : 16; HCF : 9

A. I only
B. II and III only
C. I and II only
D. I and III only
E. I, II and III

We need to keep two things in mind here:

1. Product of two numbers = LCM*HCF
2. LCM should be a multiple of HCF

Only Statement I follows these two rules.
Correct Option A
##### General Discussion
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Re: If the product of two positive integers is 144, which of the following  [#permalink]

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14 Mar 2016, 04:20
1
Superb Question...
Absolutely Amazing ..
it tests all you know about LCM and HCF/GCD
Here LCM *GCD = product of 2 numbers and this property is satisfied by all the options
But don't be fooled here.
Remember => LCM entirely contains the GCD or in other words => GCD*P=LCM for some integer P
hence GCD must completely divide the LCM
hence A is Correct.
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Re: If the product of two positive integers is 144, which of the following  [#permalink]

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09 Mar 2016, 19:59
Is the answer 'E'. Product of any two numbers is equal to the product of LCM and HCF.

All the options satisfy this condition
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Re: If the product of two positive integers is 144, which of the following  [#permalink]

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10 Mar 2016, 10:46
FACTORISING 144 will give :
2*2*2*2*3* 3

if 2 numbers are to be multipled such that a* b = 144
HCF in this case could only be 6

Thus Ans : A
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Re: If the product of two positive integers is 144, which of the following  [#permalink]

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14 Mar 2016, 04:21
Is the answer 'E'. Product of any two numbers is equal to the product of LCM and HCF.

All the options satisfy this condition

Correct but can LCM/GCD not be an integer?
Remember we must always check both the properties.

Regards
Stone Cold
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Re: If the product of two positive integers is 144, which of the following  [#permalink]

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25 Mar 2016, 11:09
2
Properties of LCM and HCF

1) HCF*LCM=a*b
2) LCM= HCF*P (where p is some integer)
3) HCF of given fractions = HCF of numerator/LCM of denominator
4) LCM of given fraction = LCM of numerator/ HCF of denominator
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Re: If the product of two positive integers is 144, which of the following  [#permalink]

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26 Nov 2018, 22:32
easy question product of two numbers = 144
hcf will be there in both numbers
eg suppose hcf is 2 for two numbers
then numbers would be in form 2*x ,2*y
only A satisfy the condition.
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Posts: 704
Re: If the product of two positive integers is 144, which of the following  [#permalink]

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25 Jan 2020, 20:20
First of all, only one is correct. Lets see how.
Given: Product of a*b= 144

option2, LCM= 18 HCF= 8
It is not possible as HCF is 2^3 but LCM contains only one 2.= 3^2*2= 18.

So now asking question that where got extra 2*2.

Similarly option 3, LCM= 2*2*2*2 and HCF is = 3*3
This can't be possible as LCM doesn't contain any 3.

So option 1 is only possible combination.

Very good learning from this problem.

Is the answer 'E'. Product of any two numbers is equal to the product of LCM and HCF.

All the options satisfy this condition
Re: If the product of two positive integers is 144, which of the following   [#permalink] 25 Jan 2020, 20:20
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# If the product of two positive integers is 144, which of the following

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