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posted by  hdupre1 on 9/17/2008 9:47:36 PM  |  status: Live  

Greast Common Divisor

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Question Details:
Let a be an integer such that (a, 72)=6 and (a, 245)=7. 
Let b= .

(a) Compute (a, b).
(b) What is the highest power of 7 which divides [a, b]?
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Sage
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posted by tdv (MNV) on 10/3/2008 1:32:00 PM  |  status: Live
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Response Details:
(a,72) = (a,  23.32) =6 implies that the highest power of 2 divides a is 1 and the highest power of 3 dividing 3 =1.
(a,245) =(a,  5.72 ) = 7 implies 5 does not divite a and and the highest power of 7 dividing a is 1.
 b=  
     = 216.39.55.77 .
(a,b) = 2.3.7 
The highest power of 7 in the [a,b] = max (1,7) =7.


                           
Tags: GCD, lcm
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