I think I understand this but I wanted to check my work! If you could please make your steps readable I would appreciate it! 3) Let a = 2°36527°, b= 243³5$11?, and e = 2'375'118. Determine, in prime factorized form,both ged(a, b, c) and lem(a, b, c).

Answered: 3) Let a = 2°36527°, b=243³5$11?, and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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I think I understand this but I wanted to check my work! If you could please make your steps readable I would appreciate it!

3) Let a = 2°36527°, b= 243³5$11?, and e = 2'375'118. Determine, in prime factorized form,
both ged(a, b, c) and lem(a, b, c).

Expert Solution

Step 1

Consider the given information.

$a = 2^{5} 3^{6} 5^{2} 7^{3}, b = 2^{4} 3^{3} 5^{8} 11^{2}, c = 2^{7} 3^{7} 5^{5} 11^{8}$

Now, calculate the GCD of for a, b and c.

$\begin{array}{rcl} g c d (a, b, c) & = & (2^{5} 3^{6} 5^{2} 7^{3}, 2^{4} 3^{3} 5^{8} 11^{2}, 2^{7} 3^{7} 5^{5} 11^{8}) \\ = & 2^{4} 3^{3} 5^{2} (2 \cdot 3^{3} 7^{3}, 5^{6} 11^{2}, 2^{3} 3^{4} 5^{3} 11^{8}) \\ = & 2^{7} 3^{7} 5^{8} 11^{8} \end{array}$

Thus, the gcd for a, b and c is $2^{7} 3^{7} 5^{8} 11^{8}$ .

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