imhimanshu wrote:
Question
The Least Common multiple of \(2^6-1\) and \(2^9-1\) is
a) 2^12+27*2^9-217
b) 2^ 12 +63*2^3-1
c) 2^12+5^29-1
d) 2^12+9*2^8 -1
e) None of these.
Hi Experts,
I would like to know what is the best approach to solve such questions.
Help will be appreciated.
Thanks
H
Responding to a pm:
The best approach in my opinion is what Zarrolou has suggested above.
LCM * GCF = Product of the numbers = \((2^6-1)*(2^9-1) = (2^3 - 1)(2^3 + 1) * (2^3 - 1)(2^6 + 1 + 2^3)\)
Notice that the only common factor between them is \((2^3 - 1)\) so this must be the GCF. Hence LCM will be the rest of the product.
\(LCM = (2^3 + 1) * (2^3 - 1)(2^6 + 1 + 2^3) = (2^6 - 1)(2^6 + 1 + 2^3)\)
Now how do you get it in the format in the options? Almost all options have \(2^{12}\) and 1 so retain those two and club everything else together.
\(LCM = 2^{12} - 1 + (2^6 + 2^9 - 2^6 - 2^3) = 2^{12} - 1 + 2^3(2^6 - 1) = 2^{12} - 1 + 2^3*63\)
Answer (B)
Note that option 'none of these' makes it more complicated since you cannot try some more esoteric methods e.g. last digit etc. GMAT doesn't give you this option. Also, GMAT doesn't expect you to know a^3 - b^3 = (a-b)(a^2 + ab + b^2). Of course, you should be able to arrive at the LHS, given the RHS.
Hence, there are very few CAT questions which will actually be GMAT relevant. If you are practicing for GMAT, try to stick to a GMAT source, especially if you have limited time.
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Karishma
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