Latest CAT Aptitude Question SOLUTION: what is the lcm of (2^2011),(2^2011+1) and (2^2011+2)

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(#M40027743) CAT question lcm Keep an EYE

what is the lcm of
(2^2011),(2^2011+1) and (2^2011+2)

Asked In CAT MAYANK AGARWAL (11 years ago)

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Sagar Mate  (11 years ago)

in 2^2011+1 is in form a^(odd)+b^(odd), which is always divisible by (a+b)
so (2+1) = 3 in our case..
.
similarly 2^2011 + 2 can be written as 2(2^2010 + 1)
AND concentrating on (2^2010 + 1) we simplify (4^1005 + 1) which is again in form a^(odd)+b^(odd), which is always divisible by (a+b)
so in this case (4+1) = 5
.
and we know 2^2011 is least divisible by 2
.
.
therefore the LCM of (2^2011) and (2^2011+1) and (2^2011+2) is 2*3*5 = 30

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lakshay bansal  (11 years ago)

lcm=(2^2011)*(2^2011+1)*(2^2010+1)
=(2^4022+2^2011)*(2^2010+1)
=2^6032+2^4022+2^4021+2^2011

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rajveer singh  (11 years ago)

2^2013 is the lcm of the given term, simply take the common out of them.

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