Latest Elitmus Aptitude Question SOLUTION: what is the lcm of ((3^501)-1),((3^501)+1)......??

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what is the lcm of ((3^501)-1),((3^501)+1)......??

Asked In Elitmus ashish (9 years ago)

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Suraj Pawar  (9 years ago)

3^501-1 and 3^501+1 are 2 consecutive even nos,so their HCF will be 2.
HCF x LCM=((3^501)-1)x((3^501)+1)
2 x LCM= (3^501)^2 - 1^2
LCM= ((3^1002)-1)/2

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Saraswathy  (9 years ago)

LCM(a^m -1, a^m +1) is
a^2m -1 , if a is even
(a^2m -1)/2 , if a is odd
Here a^2m -1 is nothing but product of 2 numbers => (a^m -1)* (a^m +1) = a^2m -1
Check for small numbers
LCM(2^3 -1 , 2^3 +1) => 2^2(3) -1 = 63 [Since a is even]
LCM(5^2 -1 , 5^2 +1) => [5^2(2) -1]/2 = 312 [since a is odd]

Hence LCM(3^501 -1, 3^501 +1) => [3^2(501) -1]/2 [Since a is odd]...

Ans : [3^1002 -1]/2

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Devraj Dad  (9 years ago)

ans will be ((3^1002)-1)/2

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