The Least Common multiple of 2^6−1 and 2^9−1 is Choose the correct choice from the following choices:
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.
The best approach in my opinion is what Zarroli 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 (23−1)(23−1) 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 (2^ 12 +63*2^3-1)
<result>B</result>
The Least Common multiple of 2^6−1 and 2^9−1 is