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

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

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New post 09 Mar 2016, 12:44
00:00
A
B
C
D
E

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  65% (hard)

Question Stats:

61% (02:05) correct 39% (01:27) wrong based on 195 sessions

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

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New post 09 Mar 2016, 21:49
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7
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
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Re: If the product of two positive integers is 144, which of the following  [#permalink]

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New post 09 Mar 2016, 20:59
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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New post 10 Mar 2016, 11:46
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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New post 14 Mar 2016, 05:20
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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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New post 14 Mar 2016, 05:21
Divyadisha wrote:
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
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Re: If the product of two positive integers is 144, which of the following  [#permalink]

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New post 25 Mar 2016, 12:09
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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New post 26 Nov 2018, 23:32
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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Re: If the product of two positive integers is 144, which of the following   [#permalink] 26 Nov 2018, 23:32
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If the product of two positive integers is 144, which of the following

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