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

Question

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

OptimusPrepJanielle · Accepted Answer

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

Divyadisha · Answer

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

All the options satisfy this condition

nipunjain14 · Answer

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

stonecold · Answer

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.

stonecold · Answer

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

Regards
Stone Cold

Vinayprajapati · Answer

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

manjot123 · Answer

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.

gvij2017 · Answer

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.

abhimanyuarya · Answer

umber is 144.

No of factors are 5*3 = 15

Square of number is 12.

No of factors before 12 are 7 numbers and after 12 are 7 numbers

1,2,3,4,6,8,9,12,16,18,24,36,48,72,144

Therefore various combinations are 
1*144 = 144
2*72 = 144
3*48=144
4*36=144
6*24=144
8*18=144
9*16=144

Among the above only option A is matching i.e. LCM 24 and HCF 6

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

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GMAT Problem Solving (PS) Questions

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

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